Probability and statistics Books

Book SynopsisIn this text on statistical decision-making, the authors use examples such as computing values for the stock market, conducting market research reports or using an options pricing model to illuminate the subject matter.Table of ContentsIntroduction to Quantitative Decision Making. Discrete Probability and Decision Analysis. Decision Making with Binomial and Normal Probabilities. Decisions Based on Sample Statistics. Sample Design and Estimation. Decisions Based on Linear Relationships. Hypothesis Testing. Quality Control. Forecasting. Analysis of Variance. Simulation. Linear Programming. Appendices. Data Disk Files. Selected References. Answers to Even-Numbered Problems. Index.

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Book SynopsisPATTERN CLASSIFICATION a unified view of statistical and neural approaches The product of years of research and practical experience in pattern classification, this book offers a theory-based engineering perspective on neural networks and statistical pattern classification. Pattern Classification sheds new light on the relationship between seemingly unrelated approaches to pattern recognition, including statistical methods, polynomial regression, multilayer perceptron, and radial basis functions. Important topics such as feature selection, reject criteria, classifier performance measurement, and classifier combinations are fully covered, as well as material on techniques that, until now, would have required an extensive literature search to locate. A full program of illustrations, graphs, and examples helps make the operations and general properties of different classification approaches intuitively understandable. Offering a lucid presentation of complex appTable of ContentsStatistical Decision Theory. Need for Approximations: Fundamental Approaches. Classification Based on Statistical Models Determined by First-and-Second Order Statistical Moments. Classification Based on Mean-Square Functional Approximations. Polynomial Regression. Multilayer Perceptron Regression. Radial Basis Functions. Measurements, Features, and Feature Section. Reject Criteria and Classifier Performance. Combining Classifiers. Conclusion. STATMOD Program: Description of ftp Package. References. Index.

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Book SynopsisUnlike other books on variance components, Statistical Tests for Mixed Linear Models continues beyond point estimation to cover hypothesis and data testing. By addressing these areas, the author presents practical applications of variance component models through testing of fixed effects and variance components.Trade Review"...compiles the available results in this area into a single volume." (Quarterly of Applied Mathematics, Vol. LIX, No. 3, September 2001) "...the authors are to be congratulated for this important and useful book...the authors state...'it will contribute to the development of the area, and enhance its exposure and usefulness.' The reviewers agree." (Mathematical Geology)Table of ContentsNature of Exact and Optimum Tests in Mixed Linear Models. Balanced Random and Mixed Models. Measures of Data Imbalance. Unbalanced One-Way and Two-Way Random Models. Random Models with Unequal Cell Frequencies in the Last Stage. Tests in Unbalanced Mixed Models. Recovery of Inter-Block Information. Split-Plot Designs Under Mixed and Random Models. Tests Using Generalized P-Values. Multivariate Mixed and Random Models. Appendix. General Bibliography. Indexes.

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Book SynopsisThis book examines the solution of some of the most common problems of numerical computation. By concentrating on one effective algorithm for each basic task, it develops the fundamental theory in a brief, elementary way. There are ample exercises, and codes are provided to reduce the time otherwise required for programming and debugging.Table of ContentsErrors and Floating Point Arithmetic. Systems of Linear Equations. Interpolation. Roots of Nonlinear Equations. Numerical Integration. Ordinary Differential Equations. Appendix. Answers to Selected Exercises. Index.

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Book SynopsisMaster the fundamental math skills necessary to quantify andevaluate a broad range of environmental questions. Environmental issues are often quantitative--how much land, howmany people, what amount of pollution. Computer programs areuseful, but there is no substitute for being able to use a simplecalculation to slice through to the crux of the problem. Having agrasp of how the factors interact and whether the results makesense allows one to explain and argue a point of view forcefully todiverse audiences. With an engaging, down-to-earth style and practical problem-solvingapproach, Ecological Numeracy makes it easy to understand andmaster basic mathematical concepts and techniques that areapplicable to life-cycle assessment, energy consumption, land use,pollution generation, and a broad range of other environmentalissues. Robert Herendeen brings the numbers to life with dozens offascinating, often entertaining examples and problems. Requiring only a moderate Table of ContentsContext and Acclimatization. Contributions to Environmental Impact: Analyzing the Components ofChange. Consequences of Exponential (Geometric) Growth. End-Use Analysis and Predicting Future Demand. Economic Considerations, Discount Rates, and Benefit-CostAnalysis. Limits. Dynamics, Stocks and Flows, Age Class Effects. Indirect Effects. Shared Resources and the Tragedy of the Commons. The Automobile: A Powerful Problem. Ecological Economics and Sustainability. Thermodynamics and Energy Efficiency. Appendices. References. Index.

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Book SynopsisThis text provides the reader with a general and widely-applicable problem solving strategy for use in quality improvement. It covers a variety of statistical and "non-statistical" problem-solving tools, and discusses techniques that are useful when problems are solved by groups or teams of people.Table of ContentsIntroduction Detecting and Prioritizing Problems Problem-Solving Strategies Group-Based Problem Solving The Reward Structure: The Human Side of Problem Solving Measurements and Their Importance for Quality Analysis of Information: Graphical Displays and Numerical Summaries Modeling Variability: An Introduction to Probability Distributions Sample Surveys Statistical Inference Under Simple Random Sampling Acceptance Sampling Plans Statistical Process Control: Control Charts Process Capability and PRE-Control Principles of Effective Experimental Design Analysis of Data from Effective Experimental Designs and an Introduction to Factorial Experiments Taguchi Design Methods for Product and Process Improvement Regression Analysis: A Useful Tool for Modeling Relationships

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Book SynopsisThis book concentrates on a variety of multivariate distributional models (other than the normal and related sampling distributions). It covers a wide range of models from multivariate (MV) exponential, MV extremevalue and MV gamma, to MV beta (or dirichlet) and MV pareto, to name but a few.Trade ReviewThis book brings one right up to date and is a worthy addition to the existing set of second editions of the other volumes of Distributions in Statistics. It will remain the key reference for many years. (Short Book Reviews, Vol. 20, No. 3, December 2000) [...] Continuous Multivariate Distributions is a unique and valuable source of information on multivariate distributions. This book, and the rest of this venerable and important series, should be on the shelves of every statistician. (JASA June 2001) For certain it will serve as the primary source for continuous multivariate statistical distributions for a long time. (Zentralblatt Math, Volume 946, No 21, 2000) "...provides a remarkably comprehensive, self-contained resource for this important statistical area." (Mathematical Reviews, Issue 2001h) "It will remain the key reference for many years." (Short Book Reviews, December 2000) "...will serve as the primary source for continuous multivariate statistical distributions for a long time." (Zentralblatt MATH, Vol. 946, No. 21) "Like its predecessors, this monograph is a most welcome addition to the statistical literature. We are looking forward to Volume 2..." (Statistical Papers, Vol. 42, No. 3, 2001)Table of ContentsSystems of Continuous Multivariate Distributions. Multivariate Normal Distributions. Bivariate and Trivariate Normal Distributions. Multivariate Exponential Distributions. Multivariate Gamma Distributions. Dirichlet and Inverted Dirichlet Distributions. Multivariate Liouville Distributions. Multivariate Logistic Distributions. Multivariate Pareto Distributions. Bivariate and Multivariate Extreme Value Distributions. Natural Exponential Families. Indexes.

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Book SynopsisBringing together business and engineering to reliability analysis With manufactured products exploding in numbers and complexity, reliability studies play an increasingly critical role throughout a product's entire life cycle-from design to post-sale support.Trade ReviewThis book provides a comprehensive overview of both qualitative and quantitative aspects of reliability. Mathematical and statistical concepts related to reliability modeling and analysis are presented along with important bibliography and a listing of resources which includes journals, reliability standards, other publications, and databases. The coverage of individual topics is not always deep, but this should be a valuable reference for any engineer or statisticial working in reliability. (Short Book Reviews, Vol.20, No. 3, December 2000) "...this should be a valuable reference for any engineer or statistician working in reliability." (Short Book Reviews, Vol. 20, No. 3, December 2000) This book presents a remarkably broad framework for the analysis of the technical and commercial aspects of product reliability.... Written by two highly respected experts in the field, this practical work provides engineers, operations managers, and applied statisticians with both qualitative and quantitative tools for solving a variety of complex, real-world reliability problems. (Zentralblatt Math, Volume 945, No 20, 2000) "...a comprehensive overview..." (Short Book Reviews, December 2000) "...an excellent textbook for an advanced course in biostatistics and also an indispensable reference for biostatisticians and epidemiologists" (Short Book Reviews, December 2000) "...an excellent book, distinguished by excellence of exposition, breadth and comprehensiveness of topical overage, relevance, number and importance of examples, depth of references, and quality of exercises...will become one of the standard references on reliability...so comprehensive...it would provide material for more than a two-semester graduate sequence...will find a warm welcome in the best graduate programs. I strongly recommend it." (Technometrics, Vol. 43, No. 4, November 2001) "I would recommend this book to practitioners and as a graduate level book." (Journal of the American Statistical Association, December 2001)Table of ContentsCONTEXT OF RELIABILITY ANALYSIS. An Overview. Illustrative Cases and Data Sets. BASIC RELIABILITY METHODOLOGY. Collection and Preliminary Analysis of Failure Data. Probability Distributions for Modeling Time to Failure. Basic Statistical Methods for Data Analysis. RELIABILITY MODELING, ESTIMATION, AND PREDICTION. Modeling Failures at the Component Level. Modeling and Analysis of Multicomponent Systems. Advanced Statistical Methods for Data Analysis. Software Reliability. Design of Experiments and Analysis of Variance. Model Selection and Validation. RELIABILITY MANAGEMENT, IMPROVEMENT, AND OPTIMIZATION. Reliability Management. Reliability Engineering. Reliability Prediction and Assessment. Reliability Improvement. Maintenance of Unreliable Systems. Warranties and Service Contracts. Reliability Optimization. EPILOGUE. Case Studies. Resource Materials. Appendices. References. Indexes.

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Book SynopsisAn exploration of regression graphics through computer graphics. Recent developments in computer technology have stimulated new and exciting uses for graphics in statistical analyses. Regression Graphics, one of the first graduate-level textbooks on the subject, demonstrates how statisticians, both theoretical and applied, can use these exciting innovations. After developing a relatively new regression context that requires few scope-limiting conditions, Regression Graphics guides readers through the process of analyzing regressions graphically and assessing and selecting models. This innovative reference makes use of a wide range of graphical tools, including 2D and 3D scatterplots, 3D binary response plots, and scatterplot matrices. Supplemented by a companion ftp site, it features numerous data sets and applied examples that are used to elucidate the theory. Other important features of this book include: * Extensive coverage of a relatively new regression conteTrade ReviewIn summary, it is a very well-written book with a good blend of theory and application. Some of the chapters in the book are very theoretical and very extensive so that a researcher in this area will benefit much from reading this book. Practitioners will also benefit by getting the basic ideas of the various concepts and understanding them through the abundant number of examples in the book. (Statistical Methods in Medical Research, 9: 602-604, 2000)Table of ContentsIntroduction to 2D Scatterplots. Constructing 3D Scatterplots. Interpreting 3D Scatterplots. Binary Response Variables. Dimension-Reduction Subspaces. Graphical Regression. Getting Numerical Help. Graphical Regression Studies. Inverse Regression Graphics. Sliced Inverse Regression. Principles Hessian Directions. Studying Predictor Effects. Predictor Transformations. Graphics for Model Assessment. Bibliography. Indexes.

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Book SynopsisOther volumes in the Wiley Series in Probability and MathematicalStatistics, Ralph A. Bradley, J. Stuart Hunter, David G. Kendall,& Geoffrey S. Watson, Advisory Editors Statistical Models inApplied Science Karl V. Bury Of direct interest to engineers andapplied scientists, this book presents general principles ofstatistics and specific distribution methods and models. Prominentdistribution properties and methods that are useful over a widerange of applications are covered in detail. The strengths andweaknesses of the distributional models are fully described, givingthe reader a firm, intuitive approach to the selection of the modelmost appropriate to the problem at hand. 1975 656 pp. FittingEquations To Data Computer Analysis of Multifactor Data forScientists and Engineers Cuthbert Daniel & Fred S. Wood Withthe assistance of John W. Gorman The purpose of this book is tohelp the serious data analyst, scientist, or engineer with acomputer to: recognize the strengths and limitations of hiTable of ContentsIntroduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three-Factor, Two-Level Experiments. Unreplicated Four-Factor, Two-Level Experiments. Three Five-Factor, Two-Level Unreplicated Experiments. Larger Two-Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, FractionalReplication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend-Robust Plans. Nested Designs. Conclusions and Apologies.

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Book SynopsisA guide to achieving business successes through statistical methods Statistical methods are a key ingredient in providing data-based guidance to research and development as well as to manufacturing. Understanding the concepts and specific steps involved in each statistical method is critical for achieving consistent and on-target performance.Trade Review"I highly recommend this book to anyone interested in applying statistics to solve problems." (Journal of Food Quality, October 2004) "…an interesting collection of material in nice summary form…" (Journal of the American Statistical Association, December 2004) "Overall, Statistical Methods for Six Sigma in R & D and Manufacturingoffers some good insights and practical views of the statistical concepts covered." (Technometrics, August 2004, Vol. 46, No. 3) "...covers a large number of useful statistical methods compactly...contains a wealth of case studies and examples..." (Food Trade Review, May 2004) “...can be used as a reference or as a self-study...also as a textbook for an engineering statistics course...recommended...” (E-Streams, Vol. 7, No. 3)Table of Contents1. Introduction. 2. Basic Statistics. 2.1 Descriptive Statistics. 2.2 Statistical Distributions. 2.3 Confidence Intervals. 2.4 Sample Size. 2.5 Tolerance Intervals. 2.6 Normality, Independence and Homoscedasticity. 3. Comparative Experiments and Regression Analysis. 3.1 Hypothesis Testing Framework. 3.2 Comparing Single Population. 3.3 Comparing Two Populations. 3.4 Comparing Multiple Populations. 3.5 Correlation. 3.6 Regression Analysis. 4. Control Charts. 4.1 Role of Control Charts. 4.2 Logic of Control Limits. 4.3 Variable Control Charts. 4.4 Attribute Control Charts. 4.5 Interpreting Control Charts. 4.6 Key Success Factors. 5. Process Capability. 5.1 Capability and Performance Indices. 5.2 E stimating Capability and Performance Indices. 5.3 Six-Sigma Goal. 5.4 Planning for Improvement. 6. Other Useful Charts. 6.1 Risk-based Control Ch arts. 6.2 Modified Control Limit Chart. 6.3 Moving Average Control Chart. 6.4 Short Run Control Charts 6.5 Charts for Non-Normal Distributions. 7. Variance Components Analysis. 7.1 Chart (Random Factor). 7.2 One-way Classification (Fixed Factor). 7.3 Structured Studies and Variance Components. 8. Quality Planning with Variance Components. 8.1 Typical Manufacturing Application. 8.2 Economic Loss Functions. 8.3 Planning for Quality Improvement. 8.4 Application to Multi-Lane Manufacturing Process. 8.5 Variance Transmission Analysis. 8.6 Application to a Factorial Design. 8.7 Variance Components and Specifications. 9. Measurement Systems Analysis. 9.1 Statistical Properties of Measurement Systems. 9.2 Acceptance Criteria. 9.3 Calibration Study. 9.4 Stability and Bias Study. 9.5 Repeatability and Reproducibility (R&R) Study. 9.6 Robustness and Intermediate Precision Studies. 9.7 Linearity Study. 9.8 Method Transfer Study. 9.9 Calculating Significant Figures. 10. What Color is Your Belt? 10.1 Test. 10.2 Answers. Appendix A: Tail Area of Unit Normal Distribution. Appendix B: Probability Points of the t Distribution with v Degrees of Freedom. Appendix C: Probability Points of the x2 Distribution with v Degrees of Freedom. Appendix D1.k Values for Two-Sided Normal Tolerance Limits. Appendix D2.k Values for One-Sided Normal Tolerance Limits. Appendix E1: Percentage Points of the F Distribution: Upper 5% Points. Appendix E2: Percentage Points of the F Distribution: Upper 2.5% Points. Appendix F: Critical Values of Hartley's Maximum F Ratio Test for Homogeneity of Variances. Appendix G: Table of Control Chart Constants. Glossary Of Symbols. References. Index.

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Book SynopsisPresenting information on logistic regression models, this work explains difficult concepts through illustrative examples. This is a solutions manual to accompany applied Logistic Regression, 2nd Edition.Table of ContentsIntroduction to the Logistic Regression Model. The Multiple Logistic Regression Model. Interpretation of the Coefficients of the Logistic Regression Model. Model-Building Strategies and Methods for Logistic Regression. Assessing the Fit of the Model. Application of Logistic Regression with Different Sampling Models. Logistic Regression for Matched Case-Control Studies. Special Topics. References. Index.

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Book SynopsisThe outgrowth of more than 40 years of experience teaching and consulting with students and active researchers in many disciplines, this is a useful guide for both students and active researchers to experimental design.Trade Review"…an excellent reference for statisticians and practitioners who would like to gain broad exposure to the tools available for studying relationships between qualitative and quantitative factors…" (Journal of the American Statistical Association, June 2005) “The level of detail is higher than in most other books on similar topics and therefore makes this one a useful reference tool.” (Short Book Reviews, Vol.25, No.1, April 2005) "I will instruct statistician reporting to me to get a copy of the book, and will keep the review copy readily available on my shelf…" (Technometrics, February 2005) "There is a moderate amount of material that is not in other design books…in addition to some tricks of the trade that appear to be new…practitioners…will find the book useful." (Journal of Quality Technology, October 2004) "...an excellent resource handbook for researchers and statisticians, providing them with the tools necessary to construct better experiments and plan more efficient investigations.” (CHOICE, October 2004)Table of ContentsPreface. Introduction. The Completely Randomized Design. Linear Models for Designed Experiments. Testing Hypotheses and Determining Sample Size. Methods of Reducing Unexplained Variation. Latin Squares. Split-Plot and Related Designs. Incomplete Block Designs. Repeated Teatments Designs. Factorial Experiments, the 2n System. Factorial Experiments, the 3n System. Analysis of Experiments Without Designed Error Terms. Confounding Effects with Blocks. Fractional Factorial Experiments. Response Surface Designs. Plackett-Burmann Hadamard Plans. The General Pn and Nonstandard Factorials. Factorial Experiments with Quantitative Factors. Plans for Which Run Order is Important. Supersaturated Plans. Sequences of Fractions of Factorials. Multi-Stage xperiments. Orthogonal Arrays and Related Structures. Factorial Plans Derived via Orthogonal Arrays. Experiments on the Computer.

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Book SynopsisThis concise summary of the statistical methods used in the analysis of survival data with censoring emphasizes recently developed nonparametric techniques; outlines methods in detail and illustrates them with actual data; discusses the theory behind each method; and includes numerous worked problems and numerical exercises.Table of ContentsIntroduction to Survival Concepts. Parametric Models. Nonparametric Methods: One Sample. Nonparametric Methods: Two Samples. Nonparametric Methods: K Samples. Nonparametric Methods: Regression. Goodness of Fit. Miscellaneous Topics. Problems. References. Index.

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Book SynopsisThis book is about the philosophy and practice of Evolutionary Operation (called EVOP for short), a simple but powerful statistical tool with wide application in industry.Table of ContentsThe Basic Ideas. Simple Statistical Principles on Which EVOP is Based. The 2^2 and 2^3 Factorial Designs. Worksheets for Two-Variable EVOP Programs. Worksheets for Three-Variable EVOP Programs. Some Aspects of the Organization of Evolutionary Operation. EVOP, Optimization, and Variations of EVOP. Comments and Questions on EVOP. Appendices. Tables. References and Bibliography. Index.

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Book SynopsisA complete guide to the theory and practical applications of probability theory An Introduction to Probability Theory and Its Applications uniquely blends a comprehensive overview of probability theory with the real-world application of that theory. Beginning with the background and very nature of probability theory, the book then proceeds through sample spaces, combinatorial analysis, fluctuations in coin tossing and random walks, the combination of events, types of distributions, Markov chains, stochastic processes, and more. The book''s comprehensive approach provides a complete view of theory along with enlightening examples along the way.Table of ContentsIntroduction: The Nature of Probability Theory. The Sample Space. Elements of Combinatorial Analysis. Fluctuations in Coin Tossing and Random Walks. Combination of Events. Conditional Probability. Stochastic Independence. The Binomial and Poisson Distributions. The Normal Approximation to the Binomial Distribution. Unlimited Sequences of Bernoulli Trials. Random Variables; Expectation. Laws of Large Numbers. Integral Valued Variables. Generating Functions. Compound Distributions. Branching Processes. Recurrent Events. Renewal Theory. Random Walk and Ruin Problems. Markov Chains. Algebraic Treatment of Finite Markov Chains. The Simplest Time-Dependent Stochastic Processes. Answers to Problems.

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Book SynopsisA unique introduction to the innovative methodology of statistical flowgraphs This book offers a practical, application-based approach to flowgraph models for time-to-event data. It clearly shows how this innovative new methodology can be used to analyze data from semi-Markov processes without prior knowledge of stochastic processes--opening the door to interesting applications in survival analysis and reliability as well as stochastic processes. Unlike other books on multistate time-to-event data, this work emphasizes reliability and not just biostatistics, illustrating each method with medical and engineering examples. It demonstrates how flowgraphs bring together applied probability techniques and combine them with data analysis and statistical methods to answer questions of practical interest. Bayesian methods of data analysis are emphasized. Coverage includes: * Clear instructions on how to model multistate time-to-event data using flowgraph models * An empTrade Review"…this is a well-written book on a novel and interesting approach to multistate modeling." (Biometrics, September 2006) "This book is one that researchers interested in techniques for multistate models, either in reliability or biometry should look at." (Journal of the American Statistical Association, September 2006) "…a real addition to the toolbox of both biostatisticians who use survival analysis and reliability engineers who do failure analysis on a regular basis." (Technometrics, February 2006) “…illustrated with interesting examples…the book is particularly welcome…” (International Statistical Institute, January 2006) "...a useful...account of the use of flowgraphy or semi-Markov parametric models in both industrial and biological applications." (Journal of Biopharmaceutical Statistics, September/October 2005) "Methods are explained comprehensively, with extensive examples…data analysts would find valuable examples here for their own applications." (Computing Reviews.com, June 2, 2005) “Fruitful medical and engineering examples and applications are presented…” (Zentralblatt Math, Vol.1055, No.06, 2005)Table of ContentsPreface. 1. Multistate Models and Flowgraph Models. 2. Flowgraph Models. 3. Inversion of Flowgraph Moment Generating Functions. 4. Censored Data Histograms. 5. Bayesian Prediction for Flowgraph Models. 6. Computation Implementation of Flowgraph Models. 7. Semi-Markov Processes. 8. Incomplete Data. 9. Flowgraph Models for Queuing Systems. Appendix: Moment Generating Functions. References. Author Index. Subject Index.

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Book SynopsisThis Set Contains: Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 1, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 2, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discrete Multivariate Distributions by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Univariate Discrete Distributions, 3rd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discover the latest advances in discrete distributions theory The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributTrade Review“With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.” (Xolosepo, 27 October 2012) "The authors continue to do a praise-worthy job of making the material accessible in the third edition. This book should be on every library's shelf." (Journal of the American Statistical Association, September 2006) "These authors have achieved considerable renown for their comprehensive books on statistical distributions." (Technometrics, August 2006) "Encyclopedic in nature, the book continues to be a valuable reference." (Mathematical Reviews, 2006d) "This is an important book that should be part of every statistician's library." (MAA Reviews, January 2, 2006)Table of ContentsPreface xvii 1 Preliminary Information 1 1.1 Mathematical Preliminaries 1 1.1.1 Factorial and Combinatorial Conventions 1 1.1.2 Gamma and Beta Functions 5 1.1.3 Finite Difference Calculus 10 1.1.4 Differential Calculus 14 1.1.5 Incomplete Gamma and Beta Functions and Other Gamma-Related Functions 16 1.1.6 Gaussian Hypergeometric Functions 20 1.1.7 Confluent Hypergeometric Functions (Kummer’s Functions) 23 1.1.8 Generalized Hypergeometric Functions 26 1.1.9 Bernoulli and Euler Numbers and Polynomials 29 1.1.10 Integral Transforms 32 1.1.11 Orthogonal Polynomials 32 1.1.12 Basic Hypergeometric Series 34 1.2 Probability and Statistical Preliminaries 37 1.2.1 Calculus of Probabilities 37 1.2.2 Bayes’s Theorem 41 1.2.3 Random Variables 43 1.2.4 Survival Concepts 45 1.2.5 Expected Values 47 1.2.6 Inequalities 49 1.2.7 Moments and Moment Generating Functions 50 1.2.8 Cumulants and Cumulant Generating Functions 54 1.2.9 Joint Moments and Cumulants 56 1.2.10 Characteristic Functions 57 1.2.11 Probability Generating Functions 58 1.2.12 Order Statistics 61 1.2.13 Truncation and Censoring 62 1.2.14 Mixture Distributions 64 1.2.15 Variance of a Function 65 1.2.16 Estimation 66 1.2.17 General Comments on the Computer Generation of Discrete Random Variables 71 1.2.18 Computer Software 73 2 Families of Discrete Distributions 74 2.1 Lattice Distributions 74 2.2 Power Series Distributions 75 2.2.1 Generalized Power Series Distributions 75 2.2.2 Modified Power Series Distributions 79 2.3 Difference-Equation Systems 82 2.3.1 Katz and Extended Katz Families 82 2.3.2 Sundt and Jewell Family 85 2.3.3 Ord’s Family 87 2.4 Kemp Families 89 2.4.1 Generalized Hypergeometric Probability Distributions 89 2.4.2 Generalized Hypergeometric Factorial Moment Distributions 96 2.5 Distributions Based on Lagrangian Expansions 99 2.6 Gould and Abel Distributions 101 2.7 Factorial Series Distributions 103 2.8 Distributions of Order-k 105 2.9 q-Series Distributions 106 3 Binomial Distribution 108 3.1 Definition 108 3.2 Historical Remarks and Genesis 109 3.3 Moments 109 3.4 Properties 112 3.5 Order Statistics 116 3.6 Approximations, Bounds, and Transformations 116 3.6.1 Approximations 116 3.6.2 Bounds 122 3.6.3 Transformations 123 3.7 Computation, Tables, and Computer Generation 124 3.7.1 Computation and Tables 124 3.7.2 Computer Generation 125 3.8 Estimation 126 3.8.1 Model Selection 126 3.8.2 Point Estimation 126 3.8.3 Confidence Intervals 130 3.8.4 Model Verification 133 3.9 Characterizations 134 3.10 Applications 135 3.11 Truncated Binomial Distributions 137 3.12 Other Related Distributions 140 3.12.1 Limiting Forms 140 3.12.2 Sums and Differences of Binomial-Type Variables 140 3.12.3 Poissonian Binomial, Lexian, and Coolidge Schemes 144 3.12.4 Weighted Binomial Distributions 149 3.12.5 Chain Binomial Models 151 3.12.6 Correlated Binomial Variables 151 4 Poisson Distribution 156 4.1 Definition 156 4.2 Historical Remarks and Genesis 156 4.2.1 Genesis 156 4.2.2 Poissonian Approximations 160 4.3 Moments 161 4.4 Properties 163 4.5 Approximations, Bounds, and Transformations 167 4.6 Computation, Tables, and Computer Generation 170 4.6.1 Computation and Tables 170 4.6.2 Computer Generation 171 4.7 Estimation 173 4.7.1 Model Selection 173 4.7.2 Point Estimation 174 4.7.3 Confidence Intervals 176 4.7.4 Model Verification 178 4.8 Characterizations 179 4.9 Applications 186 4.10 Truncated and Misrecorded Poisson Distributions 188 4.10.1 Left Truncation 188 4.10.2 Right Truncation and Double Truncation 191 4.10.3 Misrecorded Poisson Distributions 193 4.11 Poisson–Stopped Sum Distributions 195 4.12 Other Related Distributions 196 4.12.1 Normal Distribution 196 4.12.2 Gamma Distribution 196 4.12.3 Sums and Differences of Poisson Variates 197 4.12.4 Hyper-Poisson Distributions 199 4.12.5 Grouped Poisson Distributions 202 4.12.6 Heine and Euler Distributions 205 4.12.7 Intervened Poisson Distributions 205 5 Negative Binomial Distribution 208 5.1 Definition 208 5.2 Geometric Distribution 210 5.3 Historical Remarks and Genesis of Negative Binomial Distribution 212 5.4 Moments 215 5.5 Properties 217 5.6 Approximations and Transformations 218 5.7 Computation and Tables 220 5.8 Estimation 222 5.8.1 Model Selection 222 5.8.2 P Unknown 222 5.8.3 Both Parameters Unknown 223 5.8.4 Data Sets with a Common Parameter 226 5.8.5 Recent Developments 227 5.9 Characterizations 228 5.9.1 Geometric Distribution 228 5.9.2 Negative Binomial Distribution 231 5.10 Applications 232 5.11 Truncated Negative Binomial Distributions 233 5.12 Related Distributions 236 5.12.1 Limiting Forms 236 5.12.2 Extended Negative Binomial Model 237 5.12.3 Lagrangian Generalized Negative Binomial Distribution 239 5.12.4 Weighted Negative Binomial Distributions 240 5.12.5 Convolutions Involving Negative Binomial Variates 241 5.12.6 Pascal–Poisson Distribution 243 5.12.7 Minimum (Riff–Shuffle) and Maximum Negative Binomial Distributions 244 5.12.8 Condensed Negative Binomial Distributions 246 5.12.9 Other Related Distributions 247 6 Hypergeometric Distributions 251 6.1 Definition 251 6.2 Historical Remarks and Genesis 252 6.2.1 Classical Hypergeometric Distribution 252 6.2.2 Beta–Binomial Distribution, Negative (Inverse) Hypergeometric Distribution: Hypergeometric Waiting-Time Distribution 253 6.2.3 Beta–Negative Binomial Distribution: Beta–Pascal Distribution, Generalized Waring Distribution 256 6.2.4 Pólya Distributions 258 6.2.5 Hypergeometric Distributions in General 259 6.3 Moments 262 6.4 Properties 265 6.5 Approximations and Bounds 268 6.6 Tables Computation and Computer Generation 271 6.7 Estimation 272 6.7.1 Classical Hypergeometric Distribution 273 6.7.2 Negative (Inverse) Hypergeometric Distribution: Beta–Binomial Distribution 274 6.7.3 Beta–Pascal Distribution 276 6.8 Characterizations 277 6.9 Applications 279 6.9.1 Classical Hypergeometric Distribution 279 6.9.2 Negative (Inverse) Hypergeometric Distribution: Beta–Binomial Distribution 281 6.9.3 Beta–Negative Binomial Distribution: Beta–Pascal Distribution, Generalized Waring Distribution 283 6.10 Special Cases 283 6.10.1 Discrete Rectangular Distribution 283 6.10.2 Distribution of Leads in Coin Tossing 286 6.10.3 Yule Distribution 287 6.10.4 Waring Distribution 289 6.10.5 Narayana Distribution 291 6.11 Related Distributions 293 6.11.1 Extended Hypergeometric Distributions 293 6.11.2 Generalized Hypergeometric Probability Distributions 296 6.11.3 Generalized Hypergeometric Factorial Moment Distributions 298 6.11.4 Other Related Distributions 299 7 Logarithmic and Lagrangian Distributions 302 7.1 Logarithmic Distribution 302 7.1.1 Definition 302 7.1.2 Historical Remarks and Genesis 303 7.1.3 Moments 305 7.1.4 Properties 307 7.1.5 Approximations and Bounds 309 7.1.6 Computation, Tables, and Computer Generation 310 7.1.7 Estimation 311 7.1.8 Characterizations 315 7.1.9 Applications 316 7.1.10 Truncated and Modified Logarithmic Distributions 317 7.1.11 Generalizations of the Logarithmic Distribution 319 7.1.12 Other Related Distributions 321 7.2 Lagrangian Distributions 325 7.2.1 Otter’s Multiplicative Process 326 7.2.2 Borel Distribution 328 7.2.3 Consul Distribution 329 7.2.4 Geeta Distribution 330 7.2.5 General Lagrangian Distributions of the First Kind 331 7.2.6 Lagrangian Poisson Distribution 336 7.2.7 Lagrangian Negative Binomial Distribution 340 7.2.8 Lagrangian Logarithmic Distribution 341 7.2.9 Lagrangian Distributions of the Second Kind 342 8 Mixture Distributions 343 8.1 Basic Ideas 343 8.1.1 Introduction 343 8.1.2 Finite Mixtures 344 8.1.3 Varying Parameters 345 8.1.4 Bayesian Interpretation 347 8.2 Finite Mixtures of Discrete Distributions 347 8.2.1 Parameters of Finite Mixtures 347 8.2.2 Parameter Estimation 349 8.2.3 Zero-Modified and Hurdle Distributions 351 8.2.4 Examples of Zero-Modified Distributions 353 8.2.5 Finite Poisson Mixtures 357 8.2.6 Finite Binomial Mixtures 358 8.2.7 Other Finite Mixtures of Discrete Distributions 359 8.3 Continuous and Countable Mixtures of Discrete Distributions 360 8.3.1 Properties of General Mixed Distributions 360 8.3.2 Properties of Mixed Poisson Distributions 362 8.3.3 Examples of Poisson Mixtures 365 8.3.4 Mixtures of Binomial Distributions 373 8.3.5 Examples of Binomial Mixtures 374 8.3.6 Other Continuous and Countable Mixtures of Discrete Distributions 376 8.4 Gamma and Beta Mixing Distributions 378 9 Stopped-Sum Distributions 381 9.1 Generalized and Generalizing Distributions 381 9.2 Damage Processes 386 9.3 Poisson–Stopped Sum (Multiple Poisson) Distributions 388 9.4 Hermite Distribution 394 9.5 Poisson–Binomial Distribution 400 9.6 Neyman Type A Distribution 403 9.6.1 Definition 403 9.6.2 Moment Properties 405 9.6.3 Tables and Approximations 406 9.6.4 Estimation 407 9.6.5 Applications 409 9.7 Pólya–Aeppli Distribution 410 9.8 Generalized Pólya–Aeppli (Poisson–Negative Binomial) Distribution 414 9.9 Generalizations of Neyman Type A Distribution 416 9.10 Thomas Distribution 421 9.11 Borel–Tanner Distribution: Lagrangian Poisson Distribution 423 9.12 Other Poisson–Stopped Sum (multiple Poisson) Distributions 425 9.13 Other Families of Stopped-Sum Distributions 426 10 Matching, Occupancy, Runs, and q-Series Distributions 430 10.1 Introduction 430 10.2 Probabilities of Combined Events 431 10.3 Matching Distributions 434 10.4 Occupancy Distributions 439 10.4.1 Classical Occupancy and Coupon Collecting 439 10.4.2 Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac Statistics 444 10.4.3 Specified Occupancy and Grassia–Binomial Distributions 446 10.5 Record Value Distributions 448 10.6 Runs Distributions 450 10.6.1 Runs of Like Elements 450 10.6.2 Runs Up and Down 453 10.7 Distributions of Order k 454 10.7.1 Early Work on Success Runs Distributions 454 10.7.2 Geometric Distribution of Order k 456 10.7.3 Negative Binomial Distributions of Order k 458 10.7.4 Poisson and Logarithmic Distributions of Order k 459 10.7.5 Binomial Distributions of Order k 461 10.7.6 Further Distributions of Order k 463 10.8 q-Series Distributions 464 10.8.1 Terminating Distributions 465 10.8.2 q-Series Distributions with Infinite Support 470 10.8.3 Bilateral q-Series Distributions 474 10.8.4 q-Series Related Distributions 476 11 Parametric Regression Models and Miscellanea 478 11.1 Parametric Regression Models 478 11.1.1 Introduction 478 11.1.2 Tweedie–Poisson Family 480 11.1.3 Negative Binomial Regression Models 482 11.1.4 Poisson Lognormal Model 483 11.1.5 Poisson–Inverse Gaussian (Sichel) Model 484 11.1.6 Poisson Polynomial Distribution 487 11.1.7 Weighted Poisson Distributions 488 11.1.8 Double-Poisson and Double-Binomial Distributions 489 11.1.9 Simplex–Binomial Mixture Model 490 11.2 Miscellaneous Discrete Distributions 491 11.2.1 Dandekar’s Modified Binomial and Poisson Models 491 11.2.2 Digamma and Trigamma Distributions 492 11.2.3 Discrete Adès Distribution 494 11.2.4 Discrete Bessel Distribution 495 11.2.5 Discrete Mittag–Leffler Distribution 496 11.2.6 Discrete Student’s t Distribution 498 11.2.7 Feller–Arley and Gegenbauer Distributions 499 11.2.8 Gram–Charlier Type B Distributions 501 11.2.9 “Interrupted” Distributions 502 11.2.10 Lost-Games Distributions 503 11.2.11 Luria–Delbrück Distribution 505 11.2.12 Naor’s Distribution 507 11.2.13 Partial-Sums Distributions 508 11.2.14 Queueing Theory Distributions 512 11.2.15 Reliability and Survival Distributions 514 11.2.16 Skellam–Haldane Gene Frequency Distribution 519 11.2.17 Steyn’s Two-Parameter Power Series Distributions 521 11.2.18 Univariate Multinomial-Type Distributions 522 11.2.19 Urn Models with Stochastic Replacements 524 11.2.20 Zipf-Related Distributions 526 11.2.21 Haight’s Zeta Distributions 533 Bibliography 535 Abbreviations 631 Index 633

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Book SynopsisComplete coverage of the prediction approach to survey sampling in a single resource Prediction theory has been extremely influential in survey sampling for nearly three decades, yet research findings on this model-based approach are scattered in disparate areas of the statistical literature.Trade Review"Valliant...is joined...to dispel the perception of dichotomy between mainstream statistics...and survey sampling..." (SciTech Book News, Vol. 24, No. 4, December 2000) "The vast majority of the book is devoted to prediction of a population mean or total, and as such it forms a cohesive and comprehensive treatment of the subject." (Mathematical Reviews, Issue 2001j) "A highly recommended book which is an essential read for all research workers in this area." (Short Book Reviews - Publication of the Int. Statistical Institute, December 2001) "This book is a welcome addition to the subject of survey sampling." (Zentralblatt MATH, Vol. 964, 2001/14)Table of ContentsIntroduction to Prediction Theory. Prediction Theory Under the General Linear Model. Bias-Robustness. Robustness and Efficiency. Variance Estimation. Stratified Populations. Models with Qualitative Auxiliaries. Clustered Populations. Robust Variance Estimation in Two-Stage Cluster Sampling. Alternative Variance Estimation Methods. Special Topics and Open Questions. Appendices. Bibliography. Answers to Select Exercises. Indexes.

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Book SynopsisWith the growing complexity of engineered systems, reliability has increased in importance throughout the twentieth century. Initially developed to meet practical needs, reliability theory has become an applied mathematical discipline that permits a priori evaluations of various reliability indices at the design stages.Table of ContentsFundamentals. Reliability Indexes. Unrepairable Systems. Load-Strength Reliability Models. Distributions with Monotone Intensity Functions. Repairable Systems. Repairable Duplicated Systems. Analysis of Performance Effectiveness. Two-Pole Networks. Optimal Redundancy. Optimal Technical Diagnosis. Additional Optimization Problems in Reliability Theory. Heuristic Methods in Reliability. Index.

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Book SynopsisRegression analysis is the study of the dependence of a response variable on one or more predictor variables. It is among the most widely used methods in statistics. In recent years, several new ways to approach regression have been presented.Trade Review"...with its up-to-date discussion of regression graphics at a very accessible level, Applied Regression Including Computing and Graphics is a must for everyone working in the area of regression analysis. I strongly recommend it as a text..." (Journal of the American Statistical Association, September 2001) "...a must for everyone working in the area of regression analysis. I strongly recommend it as a text..." (Journal of the American Statistical Association, September 2001)Table of ContentsLooking Forward and Back. Introduction to Regression. Introduction to Smoothing. Bivariate Distributions. Two-Dimensional Plots. TOOLS. Simple Linear Regression. Introduction to Multiple Linear Regression. Three-Dimensional Plots. Weights and Lack-of-Fit. Understanding Coefficients. Relating Mean Functions. Factors and Interactions. Response Transformations. Diagnostics I: Curvature and Nonconstant Variance. Diagnostics II: Influence and Outliers. Predictor Transformations. Model Assessment. REGRESSION GRAPHICS. Visualizing Regression. Visualizing Regression with Many Predictors. Graphical Regression. LOGISTIC REGRESSION AND GENERALIZED LINEAR MODELS. Binomial Regression. Graphical and Diagnostic Methods for Logistic Regression. Generalized Linear Models. Appendix. References. Indexes.

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Book SynopsisThis text combines lucid and statistically engaging exposition, graphic and applied examples, and realistic exercise settings, to take students past the mechanics of introductory-level statistical techniques into the realm of practical data analysis, and inference-based problem solving.Trade Review"...a superb book....Wild & Seber have now raised the standard of introductory textbooks another notch." (Australian & New Zealand, 2000)Table of ContentsWhat Is Statistics? Tools for Exploring Univariate Data. Exploratory Tools for Relationships. Probabilities and Proportions. Discrete Random Variables. Continuous Random Variables. Sampling Distributions of Estimates. Confidence Intervals. Significance Testing: Using Data to Test Hypotheses. Data on a Continuous Variable. Tables of Counts. Relationships between Quantitative Variables: Regression and Correlation. Control Charts. Time Series. Appendices. References. Answers to Selected Problems. Index.

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Book SynopsisThis revised and updated volume describes methods fundamental to the theory and explanation of data analysis. This edition includes extensions and devices such as component and component-plus residual plots, cross-verification with a second sample and an index of required x-precision.Trade Review"...a grand historical document for industrial statistics in its glory days, as its selection for the Classics Library implies." --Technometrics Vol. 42, No. 4 May 2001 This book provides an excellent insight into the minds of two master craftsmen at work. I very much applaud the decision to include this in a "classics library" and would encourage more authors to produce statistics books in the same vein, i.e. focused on the practical application of the subject rather than methodology development. Anyone involved in the analysis of unbalanced multifactor dtaa will find this book an extremely useful source of practical advice. --The Statistician 50 (1) 2001.Table of ContentsAssumptions and Methods of Fitting Equations. One Independent Variable. Two or More Independent Variables. Fitting an Equation in Three Independent Variables. Selection of Independent Variables. Some Consequences of the Disposition of the Data Points. Selection of Variables in Nested Data. Nonlinear Least Squares, a Complex Example. Glossary. User's Manual. Bibliography. Index.

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Book SynopsisThis book illustrates scientific methodology through descriptions of how actual scientists create science. The authors present a novel point of view, arguing that the popular perception of science as being strictly objective is untrue and that knowledge is often acquired through very personal means.Trade Review"Press and Tanur argue that subjectivity has not only played a significant role in the advancement of science, but that science will advance more rapidly if the modern methods of Bayesian statistical analysis replace some of the more classical twentieth-century methods." (SciTech Book News, Vol. 25, No. 3, September 2001) "An insightful work." (Choice, Vol. 39, No. 4, December 2001) "compilation of interesting and popular problems" (Short Book Reviews - Publication of the Int. Statistical Institute, December 2001) "...this book is fascinating." (Short Book Reviews, Vol. 21, No. 3, December 2001) "...highlight the role of subjectivity in science by describing the life and works of 17 scientists." (Zentralblatt MATH, Vol. 973, 2001/23)Table of ContentsPrefaceix 1. Introduction 1 2. Selecting the Scientists 17 3. Some Well Known Stories of Extreme Subjectivity 23 3.1 Introduction 23 3.2 Johannes Kepler 23 3.3 Gregor Mendel 26 3.4 Robert Millikan 34 3.5 Cyril Burt 37 3.6 Margaret Mead 43 4. Stories of Famous Scientists 49 4.1 Introduction 49 4.2 Aristotle 51 4.3 Galileo Galilei 60 4.4 William Harvey 71 4.5 Sir Isaac Newton 81 4.6 Antoine Lavoisier 95 4.7 Alexander von Humboldt 110 4.8 Michael Faraday 121 4.9 Charles Darwin 128 4.10 Louis Pasleur 143 4.11 Sigmund Freud 156 4.12 Marie Curie 166 4.13 Albert Einstein 177 4.14 Same Conjecrures About the Scientists 189 5. Subjectivity .in Science in Modern Times: The Bayesian Approach199 Appendix: References by Field of Application for Bayesian Statistical Science225 Bibliography 231 Subject Index 249 Name Index 267

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Book SynopsisThe information contained in this book has served as the basis for a graduate-level biostatistics class at the University of North Carolina at Chapel Hill. The book focuses in the General Linear Model (GLM) theory, stated in matrix terms, which provides a more compact, clear, and unified presentation of regression of ANOVA than do traditional sums of squares and scalar equations. The book contains a balanced treatment of regression and ANOVA yet is very compact. Reflecting current computational practice, most sums of squares formulas and associated theory, especially in ANOVA, are not included. The text contains almost no proofs, despite the presence of a large number of basic theoretical results. Many numerical examples are provided, and include both the SAS code and equivalent mathematical representation needed to produce the outputs that are presented. All exercises involve only real data, collected in the course of scientific research. The book is divided Trade Review“…very useful to applied scientists and for graduate level courses in areas of non-mathematical statistics…” (Zentralblatt Math, Vol.1039, No.8, 2004)Table of ContentsPreface. Examples and Limits of the GLM. Statement of the Model, Estimation, and Testing. Some Distributions for the GLM. Multiple Regression: General Considerations. Testing Hypotheses in Multiple Regression. Correlations. GLM Assumption Diagnostics. GLM Computation Diagnostics. Polynomial Regression. Transformations. Selecting the Best Model. Coding Schemes for Regression. One-Way ANOVA. Complete, Two-Way Factorial ANOVA. Special Cases of Two-Way ANOVA and Random Effects Basics. The Full Model in Every Cell (ANCOVA as a Special Case). Understanding and Computing Power for the GLM. Appendix A. Matrix Algebra for Linear Models. Appendix B. Statistical Tables. Appendix C. Study Guide for Linear Model Theory. Appendix D. Homework and Example Data. Appendix E. Introduction to SAS/IML. Appendix F. A Brief Manual to LINMOD. Appendix G. SAS/IML Power Program User's Guide. Appendix H. Regression Model Selection Data. References. Index.

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Book SynopsisFast technological advances have allowed investors and traders to make increasingly sophisticated analysis of market momentum. The current trend in the financial world continues towards momentum analysis. This book looks at both the theory and the application.Table of ContentsTHEORY. Introduction. Momentum Preliminaries. Indicator Creation. Indicator Selection. Indicator Combination. System Maintenance. Risk Management. Summary. APPLICATION. Spreadsheet Preliminaries. How to Apply Indicator Creation. How to Apply Indicator Selection. How to Apply Indicator Combination. Performance and Maintenance. Appendix 1: Excel Functions. Appendix 2: Indicator Variations. Glossary. Index.

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Book SynopsisIn modern society, we are ever more aware of the environmentalissues we face, whether these relate to global warming, depletionof rivers and oceans, despoliation of forests, pollution of land,poor air quality, environmental health issues, etc. At the mostfundamental level it is necessary to monitor what is happening inthe environment - collecting data to describe the changingscene. More importantly, it is crucial to formally describe theenvironment with sound and validated models, and to analyse andinterpret the data we obtain in order to take action. Environmental Statistics provides a broad overview of thestatistical methodology used in the study of the environment,written in an accessible style by a leading authority on thesubject. It serves as both a textbook for students of environmentalstatistics, as well as a comprehensive source of reference foranyone working in statistical investigation of environmentalissues. * Provides broad coverage of the methodology used in tTrade Review"Inspired by the Encyclopedia of Statistical Sciences, SecondEdition (ESS2e), this volume presents a concise, well-rounded focuson the statistical concepts and applications that are essential forunderstanding gathered data in the fields of engineering, qualitycontrol, and the physical sciences. The book successfully upholdsthe goals of ESS2e by combining both previously-published and newlydeveloped contributions written by over 100 leading academics,researchers, and practitioner in a comprehensive, approachableformat. The result is a succinct reference that unveils modern,cutting-edge approaches to acquiring and analyzing data acrossdiverse subject areas within these three disciplines, includingoperations research, chemistry, physics, the earth sciences,electrical engineering, and quality assurance." (Finwin, 7September 2011) "In this book, Vic Barnett, a distinguished environmentalstatistician, provides an overview of statistical methods that havebeen used on such problems in the environmental sciences."(Journal of the American Statistical Association, September2006) "...combines sound fundamentals and their applications."(European Journal of Soil Science, No.56, April 2005) "Many tables, graphs and figures illustrate the environmentalapplications of the statistical methods that are described."(Journal of the Royal Statistical Society, Series A,Vol.168, No.2, March 2005) "...well written...methods are illustrated with interestingexamples...a comprehensive reference source for anyone working onenvironmental issues..." (Short Book Reviews, Vol.24, No.3,December 2004) "Statisticians should enjoy the book. The author is an extremelyknowledgeable statistician, and he is writing about an applicationdomain that he clearly knows." (Technometrics, November2004) "An excellent book. Highly recommended." (Choice, July2004) "...this provides an excellent sketch of the current state ofdevelopment for new statistical methodologies...a valuableresource..." (Statistics in Medicine, 15th August 2005)Table of ContentsPreface. Chapter 1: Introduction. 1.1 Tomorrow is too Late! 1.2 Environmental Statistics. 1.3 Some Examples. 1.3.1 ‘Getting it all together’. 1.3.2 ‘In time and space’. 1.3.3 ‘Keep it simple’. 1.3.4 ‘How much can we take?’ 1.3.5 ‘Over the top’. 1.4 Fundamentals. 1.5 Bibliography. PART I: EXTREMAL STRESSES: EXTREMES, OUTLIERS, ROBUSTNESS. Chapter 2: Ordering and Extremes: Applications, models, inference. 2.1 Ordering the Sample. 2.1.1 Order statistics. 2.2 Order-based Inference. 2.3 Extremes and Extremal Processes. 2.3.1 Practical study and empirical models; generalized extreme-value distributions. 2.4 Peaks over Thresholds and the Generalized Pareto Distribution. Chapter 3: Outliers and Robustness. 3.1 What is an Outlier? 3.2 Outlier Aims and Objectives. 3.3 Outlier-Generating Models. 3.3.1 Discordancy and models for outlier generation. 3.3.2 Tests of discordancy for specific distributions. 3.4 Multiple Outliers: Masking and Swamping. 3.5 Accommodation: Outlier-Robust Methods. 3.6 A Possible New Approach to Outliers. 3.7 Multivariate Outliers. 3.8 Detecting Multivariate Outliers. 3.8.1 Principles. 3.8.2 Informal methods. 3.9 Tests of Discordancy. 3.10 Accommodation. 3.11 Outliers in linear models. 3.12 Robustness in General. PART II: COLLECTING ENVIRONMENTAL DATA: SAMPLING AND MONITORING. Chapter 4: Finite-Population Sampling. 4.1 A Probabilistic Sampling Scheme. 4.2 Simple Random Sampling. 4.2.1 Estimating the mean, &Xmacr;. 4.2.2 Estimating the variance, S2. 4.2.3 Choice of sample size, n. 4.2.4 Estimating the population total, XT. 4.2.5 Estimating a proportion, P. 4.3 Ratios and Ratio Estimators. 4.3.1 The estimation of a ratio. 4.3.2 Ratio estimator of a population total or mean. 4.4 Stratified (simple) Random Sampling. 4.4.1 Comparing the simple random sample mean and the stratified sample mean. 4.4.2 Choice of sample sizes. 4.4.3 Comparison of proportional allocation and optimum allocation. 4.4.4 Optimum allocation for estimating proportions. 4.5 Developments of Survey Sampling. Chapter 5: Inaccessible and Sensitive Data. 5.1 Encountered Data. 5.2 Length-Biased or Size-Biased Sampling and Weighted Distributions. 5.2.1 Weighted distribution methods. 5.3 Composite Sampling. 5.3.1 Attribute Sampling. 5.3.2 Continuous variables. 5.3.3 Estimating mean and variance. 5.4 Ranked-Set Sampling. 5.4.1 The ranked-set sample mean. 5.4.2 Optimal estimation. 5.4.3 Ranked-set sampling for normal and exponential distributions. 5.4.4 Imperfect ordering. Chapter 6: Sampling in the Wild. 6.1 Quadrat Sampling. 6.2 Recapture Sampling. 6.2.1 The Petersen and Chapman estimators. 6.2.2 Capture–recapture methods in open populations. 6.3 Transect Sampling. 6.3.1 The simplest case: strip transects. 6.3.2 Using a detectability function. 6.3.3 Estimating f (y). 6.3.4 Modifications of approach. 6.3.5 Point transects or variable circular plots. 6.4 Adaptive Sampling. 6.4.1 Simple models for adaptive sampling. Part III: EXAMINING ENVIRONMENTAL EFFECTS: STIMULUS–RESPONSE RELATIONSHIPS. Chapter 7: Relationship: regression-type models and methods. 7.1 Linear Models. 7.1.1 The linear model. 7.1.2 The extended linear model. 7.1.3 The normal linear model. 7.2 Transformations. 7.2.1 Looking at the data. 7.2.2 Simple transformations. 7.2.3 General transformations. 7.3 The Generalized Linear Model. Chapter 8: Special Relationship Models, Including Quantal Response and Repeated Measures. 8.1 Toxicology Concerns. 8.2 Quantal Response. 8.3 Bioassay. 8.4 Repeated Measures. Part IV: STANDARDS AND REGULATIONS. Chapter 9: Environmental Standards. 9.1 Introduction. 9.2 The Statistically Verifiable Ideal Standard. 9.2.1 Other sampling methods. 9.3 Guard Point Standards. 9.4 Standards Along the Cause–Effect Chain. Part V: A MANY-DIMENSIONAL ENVIRONMENT: SPATIAL AND TEMPORAL PROCESSES. Chapter 10: Time-Series Methods. 10.1 Space and Time Effects. 10.2 Time Series. 10.3 Basic Issues. 10.4 Descriptive Methods. 10.4.1 Estimating or eliminating trend. 10.4.2 Periodicities. 10.4.3 Stationary time series. 10.5 Time-Domain Models and Methods. 10.6 Frequency-Domain Models and Methods. 10.6.1 Properties of the spectral representation. 10.6.2 Outliers in time series. 10.7 Point Processes. 10.7.1 The Poisson process. 10.7.2 Other point processes. Chapter 11: Spatial Methods for Environmental Processes. 11.1 Spatial Point Process Models and Methods. 11.2 The General Spatial Process. 11.2.1 Predication, interpolation and kriging. 11.2.2 Estimation of the variogram. 11.2.3 Other forms of kriging. 11.3 More about Standards Over Space and Time. 11.4 Relationship. 11.5 More about Spatial Models. 11.5.1 Types of spatial model. 11.5.2 Harmonic analysis of spatial processes. 11.6 Spatial Sampling and Spatial Design. 11.6.1 Spatial sampling. 11.6.2 Spatial design. 11.7 Spatial-Temporal Models and Methods. References. Index.

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Book SynopsisNonlinear Bayesian modelling is a relatively new field, but one that has seen a recent explosion of interest. Nonlinear models offer more flexibility than those with linear assumptions, and their implementation has now become much easier due to increases in computational power. Bayesian methods allow for the incorporation of prior information, allowing the user to make coherent inference. Bayesian Methods for Nonlinear Classification and Regression is the first book to bring together, in a consistent statistical framework, the ideas of nonlinear modelling and Bayesian methods. * Focuses on the problems of classification and regression using flexible, data-driven approaches. * Demonstrates how Bayesian ideas can be used to improve existing statistical methods. * Includes coverage of Bayesian additive models, decision trees, nearest-neighbour, wavelets, regression splines, and neural networks. * Emphasis is placed on sound implementation of nonlinear models. * DiscussTrade Review"The exercises and the excellent presentation style make this book qualified t be a textbook in a graduate level nonlinear regression course." (Journal of Statistical Computation and Simulation, July 2005) "Its in-depth coverage of implementation issues and detailed discussion of pros and cons of different modeling strategies make it attractive for many researchers.” (Technometrics, May 2004) "...a fascinating account of a rapidly evolving area of statistics..." (Short Book Reviews, December 2002) "...will benefit researchers...also suitable for graduate students..." (Mathematical Reviews, 2003m)Table of ContentsPreface Acknowledgements. Introduction Bayesian Modelling Curve Fitting Surface Fitting Classification using Generalised Nonlinear Models Bayesian Tree Models Partition Models Nearest-Neighbour Models Multiple Response Models Appendix A: Probability Distributions Appendix B: Inferential Processes References Index Author Index

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Book SynopsisWith meta-analysis methods playing a crucial role in health research in recent years, this important and clearly-written book provides a much-needed survey of the field. Meta-analysis provides a framework for combining the results of several clinical trials and drawing inferences about the effectiveness of medical treatments.Trade Review“Both books can be recommended for graduate training and are useful additions to the library of those interested in the meta-analytic accumulation of literatures on training, vocational learning, and education in the professions.” (Vocations and Learning, 15 December 2010) "This well-written book offers an exhaustive criticism and up-to-date references, illustrates effectively with real life examples and data…" (Journal of Statistical Computation & Simulation, July 2004) "this is an excellent book..." (Short Book Reviews, April 2001) "...recommended for mathematically skilled readers interested in getting an overview of the various methods and the existing literature..." (Statistics in Medicine, 15 October 2003) Table of ContentsPART A: META-ANALYSIS METHODOLOGY: THE BASICS Introduction: Meta-analysis: Its Development and Uses Defining Outcome Measures used for Combining via Meta-analysis Random Effects Models for Combining Study Estimates Exploring Between Study Heterogeneity Publication Bias Study Quality Sensitivity Analysis Reporting the Results of a Meta-analysis Fixed Effects Methods for Combining Study Estimates PART B: ADVANCED AND SPECIALIZED META-ANALYSIS TOPICS Bayesian Methods in Meta-analysis Meta Regression Meta-analysis of Different Types of Data Incorporating Study Quality into a Meta-analysis Meta-analysis of Multiple and Correlated Outcome Measures Meta-analysis of Epidemiological and other Observational Studies Generalised Synthesis of Evidence - Combining Different Sources of Evidence Meta-analysis of Survival Data Cumulative Meta-analysis Miscellaneous and Developing Areas of Applications in Meta-Analysis Appendix I: Software Used for the Examples in this Book

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Book SynopsisQueueing Systems Volume 1: Theory Leonard Kleinrock This book presents and develops methods from queueing theory in sufficient depth so that students and professionals may apply these methods to many modern engineering problems, as well as conduct creative research in the field.Table of ContentsA Queueing Theory Primer. Bounds. Inequalities and Approximations. Priority Queueing. Computer Time-Sharing and Multiaccess Systems. Computer-Communication Networks: Analysis and Design. Computer-Communication Networks: Measurement, Flow Control, and ARPANET Traps.

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Book SynopsisThis work covers stochastic order relations, which provide insight into the behaviour of complex stochastic (random) systems and enables the user to collect comparative data. Application areas include queuing systems, actuarial and financial risk, decision making, and stochastic simulation.Trade Review"…a noteworthy contribution to applied probability, and I would recommend it to anyone interested in applied stochastic modeling." (Journal of the American Statistical Association, June 2005) “…will replace the excellent but now slightly dated text by Shaked and Shathikumar (1994) as the standard reference on stochastic orders.” (Statistical Papers, Vol.46, No.1, January 2005) "...provides an up-to-date survey of a notable area..." (Mathematical Reviews, 2003d) "...discusses the major concepts related to stochastic orders..." (SciTech Book News, Vol. 26, No. 2, June 2002) "...a very timely and methodically orientated book..." (Zentralblatt Math, Vol.999, No.24, 2002)Table of ContentsPreface. Univariate Stochastic Orders Theory of Integral Stochastic Orders Multivariate Stochastic Orders Stochastic Models, Comparison and Monotonicity Monotonicity and Comparability of Stochastic Processes Monotonicity Properties and Bounds for Queueing Systems Applications to Various Stochastic Models Comparing Risks. List of Symbols. References. Index.

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Book SynopsisAll students and researchers in environmental and biological sciences require statistical methods at some stage of their work. Many have a preconception that statistics are difficult and unpleasant and find that the textbooks available are difficult to understand. Practical Statistics for Environmental and Biological Scientists provides a concise, user-friendly, non-technical introduction to statistics. The book covers planning and designing an experiment, how to analyse and present data, and the limitations and assumptions of each statistical method. The text does not refer to a specific computer package but descriptions of how to carry out the tests and interpret the results are based on the approaches used by most of the commonly used packages, e.g. Excel, MINITAB and SPSS. Formulae are kept to a minimum and relevant examples are included throughout the text.Trade Review"The reassuring tone and straightforward approach of the book would be a useful guide...” (Biochemistry and Molecular Education, July/August 2002) "...covers the basics of designing an experiment/survey, data analysis and presentation, and specific methods." (SciTech Book News, Vol. 26, No. 2, June 2002) "...a good and clear exposition of basic statistical techniques..." (Biometrics, December 2002) "…This no-nonsense approach to elementary statistics should get you or your student started…" (European Journal of Soil Science, March 2003) "...This book provides a concise, userfriendly, non-technical introduction to statistics". (Metrohm Information, Vol.32, No.1, 2003)Table of ContentsPreface ix Part I Statistics Basics 1 1 Introduction 3 1.1 Do you need statistics? 3 1.2 What is statistics? 4 1.3 Some important lessons I have learnt 5 1.4 Statistics is getting easier 6 1.5 Integrity in statistics 7 1.6 About this book 8 2 A Brief Tutorial on Statistics 9 2.1 Introduction 9 2.2 Variability 9 2.3 Samples and populations 10 2.4 Summary statistics 11 2.5 The basis of statistical tests 19 2.6 Limitations of statistical tests 24 3 Before You Start 27 3.1 Introduction 27 3.2 What statistical methods are available? 28 3.3 Surveys and experiments 33 3.4 Designing experiments and surveys — preliminaries 35 3.5 Summary 43 4 Designing an Experiment or Survey 45 4.1 Introduction 45 4.2 Sample size 45 4.3 Sampling 50 4.4 Experimental design 56 4.5 Further reading 60 5 Exploratory Data Analysis and Data Presentation 63 5.1 Introduction 63 5.2 Column graphs 65 5.3 Line graphs 67 5.4 Scatter graphs 69 5.5 General points about graphs 71 5.6 Tables 73 5.7 Standard errors and error bars 74 6 Common Assumptions or Requirements of Data for Statistical Tests 77 6.1 Introduction 77 6.2 Common assumptions 81 6.3 Transforming data 84 Part II Statistical Methods 91 7 t-tests and F-tests 93 7.1 Introduction 93 7.2 Limitations and assumptions 94 7.3 t-tests 95 7.4 F-test 103 7.5 Further reading 105 8 Analysis of Variance 107 8.1 Introduction 107 8.2 Limitations and assumptions 109 8.3 One-way ANOVA 111 8.4 Multiway ANOVA 119 8.5 Further reading 127 9 Correlation and Regression 129 9.1 Introduction 129 9.2 Limitations and assumptions 130 9.3 Pearson’s product moment correlation 131 9.4 Simple linear regression 135 9.5 Correlation or regression? 142 9.6 Multiple linear regression 143 9.7 Comparing two lines 146 9.8 Fitting curves 148 9.9 Further reading 151 10 Multivariate ANOVA 153 10.1 Introduction 153 10.2 Limitations and assumptions 154 10.3 Null hypothesis 156 10.4 Description of the test 156 10.5 Interpreting the results 158 10.6 Further reading 161 11 Repeated Measures 163 11.1 Introduction 163 11.2 Methods for analysing repeated measures data 166 11.3 Designing repeated measures experiments 170 11.4 Further reading 170 12 Chi-square Tests 173 12.1 Introduction 173 12.2 Limitations and assumptions 174 12.3 Goodness of fit test 175 12.4 Test for association between two factors 178 12.5 Comparing proportions 181 12.6 Further reading 184 13 Non-parametric Tests 185 13.1 Introduction 185 13.2 Limitations and assumptions 188 13.3 Mann—Whitney U-test 189 13.4 Two-sample Kolmogorov—Smirnov test 191 13.5 Two-sample sign test 193 13.6 Kruskal—Wallis test 195 13.7 Friedman’s test 198 13.8 Spearman’s rank correlation 200 13.9 Further reading 203 14 Principal Component Analysis 205 14.1 Introduction 205 14.2 Limitations and assumptions 207 14.3 Description of the method 207 14.4 Interpreting the results 209 14.5 Further reading 218 15 Cluster Analysis 221 15.1 Introduction 221 15.2 Limitations and assumptions 222 15.3 Clustering observations 223 15.4 Clustering variables 226 15.5 Further reading 228 Appendices 229 A Calculations for statistical tests 231 B Concentration data for Chapters 14 and 15 247 C Using computer packages 249 D Choosing a test: decision table 261 E List of worked examples 265 Bibliography 271 Index 273

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Book SynopsisThe author presents a well tested approach using real examples taken from bio-medical research. He breaks down each problem into its components and where an unbiased partial test is found to exist, nonparametric combination methodology is used to determine overall solutions.Trade Review"the book is well written. It cand be useful and recommended for researchers and practitioners in a number of scientific disciplines...and for graduate students..." (Zentralblatt MATH, Vol.972, No.12, 2001) "...carefully presents a concise and mathematically rigorous treatment of permutation testing...could be used for a mathematically oriented graduate class...will form a source of recent reference material for research workers..." (Short Book Reviews, Vol. 22, No. 1, April 2002) "This book may herald a new era in biostatistics..." (Psychotherpay and Psychosomatics, September/October 2002) "...graduate and post-graduate students in some areas of physics and chemistry can benefit greatly from reading and using this book..." (The Statistician, Date Unknown)Table of ContentsPreface. Notation and Abbreviations. Introduction. Discussion of a Simple Testing Problem. Theory of Permutation Tests for One-Sample Problems. Examples of Univariate Multi-Sample Problems. Theory of Permutation Tests for Multi-Sample Problems. Nonparametric Combination Methodology. Examples of Nonparametric Combination. Permutation Analysis in Factorial Designs. Permutation Testing with Missing Data. The Behrens--Fisher Permutation Problem. Permutation Testing for Repeated Measurements. Further Applications. References. Index.

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Book SynopsisA guide which uses a problem solving approach and shows how to implement Monte Carlo methods, starting from first principles to advanced techniques.Table of ContentsPreface xi Acknowledgements xiii Mathematical Notation xv 1 Introduction 1 2 The Mathematics Behind Monte Carlo Methods 5 2.1 A Few Basic Terms in Probability and Statistics 5 2.2 Monte Carlo Simulations 7 2.2.1 Monte Carlo Supremacy 8 2.2.2 Multi-dimensional Integration 8 2.3 Some Common Distributions 9 2.4 Kolmogorov’s Strong Law 18 2.5 The Central Limit Theorem 18 2.6 The Continuous Mapping Theorem 19 2.7 Error Estimation for Monte Carlo Methods 20 2.8 The Feynman–Kac Theorem 21 2.9 The Moore–Penrose Pseudo-inverse 21 3 Stochastic Dynamics 23 3.1 Brownian Motion 23 3.2 Itô’s Lemma 24 3.3 Normal Processes 25 3.4 Lognormal Processes 26 3.5 The Markovian Wiener Process Embedding Dimension 26 3.6 Bessel Processes 27 3.7 Constant Elasticity Of Variance Processes 28 3.8 Displaced Diffusion 29 4 Process-driven Sampling 31 4.1 Strong versus Weak Convergence 31 4.2 Numerical Solutions 32 4.2.1 The Euler Scheme 32 4.2.2 The Milstein Scheme 33 4.2.3 Transformations 33 4.2.4 Predictor–Corrector 35 4.3 Spurious Paths 36 4.4 Strong Convergence for Euler and Milstein 37 5 Correlation and Co-movement 41 5.1 Measures for Co-dependence 42 5.2 Copulæ 45 5.2.1 The Gaussian Copula 46 5.2.2 The t-Copula 49 5.2.3 Archimedean Copulae 51 6 Salvaging a Linear Correlation Matrix 59 6.1 Hypersphere Decomposition 60 6.2 Spectral Decomposition 61 6.3 Angular Decomposition of Lower Triangular Form 62 6.4 Examples 63 6.5 Angular Coordinates on a Hypersphere of Unit Radius 65 7 Pseudo-random Numbers 67 7.1 Chaos 68 7.2 The Mid-square Method 72 7.3 Congruential Generation 72 7.4 Ran0 To Ran3 74 7.5 The Mersenne Twister 74 7.6 Which One to Use? 75 8 Low-discrepancy Numbers 77 8.1 Discrepancy 78 8.2 Halton Numbers 79 8.3 Sobol’ Numbers 80 8.3.1 Primitive Polynomials Modulo Two 81 8.3.2 The Construction of Sobol’ Numbers 82 8.3.3 The Gray Code 83 8.3.4 The Initialisation of Sobol’ Numbers 85 8.4 Niederreiter (1988) Numbers 88 8.5 Pairwise Projections 88 8.6 Empirical Discrepancies 91 8.7 The Number of Iterations 96 8.8 Appendix 96 8.8.1 Explicit Formula for the L2-norm Discrepancy on the Unit Hypercube 96 8.8.2 Expected L2-norm Discrepancy of Truly Random Numbers 97 9 Non-uniform Variates 99 9.1 Inversion of the Cumulative Probability Function 99 9.2 Using a Sampler Density 101 9.2.1 Importance Sampling 103 9.2.2 Rejection Sampling 104 9.3 Normal Variates 105 9.3.1 The Box–Muller Method 105 9.3.2 The Neave Effect 106 9.4 Simulating Multivariate Copula Draws 109 10 Variance Reduction Techniques 111 10.1 Antithetic Sampling 111 10.2 Variate Recycling 112 10.3 Control Variates 113 10.4 Stratified Sampling 114 10.5 Importance Sampling 115 10.6 Moment Matching 116 10.7 Latin Hypercube Sampling 119 10.8 Path Construction 120 10.8.1 Incremental 120 10.8.2 Spectral 122 10.8.3 The Brownian Bridge 124 10.8.4 A Comparison of Path Construction Methods 128 10.8.5 Multivariate Path Construction 131 10.9 Appendix 134 10.9.1 Eigenvalues and Eigenvectors of a Discrete-time Covariance Matrix 134 10.9.2 The Conditional Distribution of the Brownian Bridge 137 11 Greeks 139 11.1 Importance Of Greeks 139 11.2 An Up-Out-Call Option 139 11.3 Finite Differencing with Path Recycling 140 11.4 Finite Differencing with Importance Sampling 143 11.5 Pathwise Differentiation 144 11.6 The Likelihood Ratio Method 145 11.7 Comparative Figures 147 11.8 Summary 153 11.9 Appendix 153 11.9.1 The Likelihood Ratio Formula for Vega 153 11.9.2 The Likelihood Ratio Formula for Rho 156 12 Monte Carlo in the BGM/J Framework 159 12.1 The Brace–Gatarek–Musiela/Jamshidian Market Model 159 12.2 Factorisation 161 12.3 Bermudan Swaptions 163 12.4 Calibration to European Swaptions 163 12.5 The Predictor–Corrector Scheme 169 12.6 Heuristics of the Exercise Boundary 171 12.7 Exercise Boundary Parametrisation 174 12.8 The Algorithm 176 12.9 Numerical Results 177 12.10 Summary 182 13 Non-recombining Trees 183 13.1 Introduction 183 13.2 Evolving the Forward Rates 184 13.3 Optimal Simplex Alignment 187 13.4 Implementation 190 13.5 Convergence Performance 191 13.6 Variance Matching 192 13.7 Exact Martingale Conditioning 195 13.8 Clustering 196 13.9 A Simple Example 199 13.10 Summary 200 14 Miscellanea 201 14.1 Interpolation of the Term Structure of Implied Volatility 201 14.2 Watch Your CPU Usage 202 14.3 Numerical Overflow and Underflow 205 14.4 A Single Number or a Convergence Diagram? 205 14.5 Embedded Path Creation 206 14.6 How Slow is Exp()? 207 14.7 Parallel Computing And Multi-threading 209 Bibliography 213 Index 219

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Book SynopsisREAD ALL ABOUT IT! David Spiegelhalter has recently joined the ranks of Isaac Newton, Charles Darwin and Stephen Hawking by becoming a fellow of the Royal Society.Originating from the Medical Research Council's biostatistics unit, David has played a leading role in the Bristol heart surgery and Harold Shipman inquiries. Order a copy of this author's comprehensive text TODAY! The Bayesian approach involves synthesising data and judgement in order to reach conclusions about unknown quantities and make predictions. Bayesian methods have become increasingly popular in recent years, notably in medical research, and although there are a number of books on Bayesian analysis, few cover clinical trials and biostatistical applications in any detail. Bayesian Approaches to Clinical Trials and Health-Care Evaluation provides a valuable overview of this rapidly evolving field, including basic Bayesian ideas, prior distributions, clinical trials, observational studies, evidence synTrade Review"This is a terrific book and should be on the shelf of every professional that works in clinical trials or health-care evaluation. It gives a thorough pragmatic introduction to Bayesian methods for health-care interventions, provides many example along with data and software to reproduce the analyses, guides readers to areas where Bayesian methods are particularly valuable, and includes an excellent set of exercises." (Journal of the American Statistical Association, June 2009) "Bayesian Approaches to Clinical Trials and Health-Care Evaluation' is a clear and comprehensive text for biostatisticians who want to understand and apply Bayesian statistical methods to clinical research." (Journal of Clinical Best Practices, Nov 2008) "…an indispensable resource for all students and investigators who plan to incorporate Bayesian methods into their research." (The Annals of Pharmacotherapy, January 2005) "...a valuable resource for libraries, and those who are involved in quantitative health care evaluation..." (Royal Statistical Society, Vol.168, No.1, January 2005) "...The technical material is presented in an accessible style, and the examples given clearly illustrate the principles under discussion..." (Short Book Reviews, Vol.24, No.3, December 2004) "...Bayesian analysis seems set to reach a wider audience with the publication of [this] introductory level text..." (Financial Times, 16 April 2004) "...very well laid-out and easy to follow...a very good resource for teaching students..." (Statistical Methods in Medical Research, Vol 14, 2005) "I would use with pleasure and interest this book as a textbook..." (Metron Journal, Vol.63, No.2, 2005) "...I can pay the authors no higher tribute than to say that I would be proud to have written this book. It is elegant and it is destined to becoming a classic in the field." (Statistics in Medicine, 15th July 2005) "...a generous supply of exercises...I recommend it very highly..." (Clinical Trials, No.1 2004) "...Bayesian analysis seems set to reach a wider audience with the publication of [this] introductory level text..." (Financial Times, 16 April 2004) "...a generous supply of exercises...I recommend it very highly..." (Clinical Trials, No.1 2004)Table of ContentsPreface. List of examples. 1. Introduction. 1.1 What are Bayesian methods? 1.2 What do we mean by ‘health-care evaluation’? 1.3 A Bayesian approach to evaluation. 1.4 The aim of this book and the intended audience. 1.5 Structure of the book. 2. Basic Concepts from Traditional Statistical Analysis. 2.1 Probability. 2.1.1 What is probability? 2.1.2 Odds and log-odds. 2.1.3 Bayes theorem for simple events. 2.2 Random variables, parameters and likelihood. 2.2.1 Random variables and their distributions. 2.2.2 Expectation, variance, covariance and correlation. 2.2.3 Parametric distributions and conditional independence. 2.2.4 Likelihoods. 2.3 The normal distribution. 2.4 Normal likelihoods. 2.4.1 Normal approximations for binary data. 2.4.2 Normal likelihoods for survival data. 2.4.3 Normal likelihoods for count responses. 2.4.4 Normal likelihoods for continuous responses. 2.5 Classical inference. 2.6 A catalogue of useful distributions*. 2.6.1 Binomial and Bernoulli. 2.6.2 Poisson. 2.6.3 Beta. 2.6.4 Uniform. 2.6.5 Gamma. 2.6.6 Root-inverse-gamma. 2.6.7 Half-normal. 2.6.8 Log-normal. 2.6.9 Student’s t. 2.6.10 Bivariate normal. 2.7 Key points. Exercises. 3. An Overview of the Bayesian Approach. 3.1 Subjectivity and context. 3.2 Bayes theorem for two hypotheses. 3.3 Comparing simple hypotheses: likelihood ratios and Bayes factors. 3.4 Exchangeability and parametric modelling*. 3.5 Bayes theorem for general quantities. 3.6 Bayesian analysis with binary data. 3.6.1 Binary data with a discrete prior distribution. 3.6.2 Conjugate analysis for binary data. 3.7 Bayesian analysis with normal distributions. 3.8 Point estimation, interval estimation and interval hypotheses. 3.9 The prior distribution. 3.10 How to use Bayes theorem to interpret trial results. 3.11 The ‘credibility’ of significant trial results*. 3.12 Sequential use of Bayes theorem*. 3.13 Predictions. 3.13.1 Predictions in the Bayesian framework. 3.13.2 Predictions for binary data*. 3.13.3 Predictions for normal data. 3.14 Decision-making. 3.15 Design. 3.16 Use of historical data. 3.17 Multiplicity, exchangeability and hierarchical models. 3.18 Dealing with nuisance parameters*. 3.18.1 Alternative methods for eliminating nuisance parameters*. 3.18.2 Profile likelihood in a hierarchical model*. 3.19 Computational issues. 3.19.1 Monte Carlo methods. 3.19.2 Markov chain Monte Carlo methods. 3.19.3 WinBUGS. 3.20 Schools of Bayesians. 3.21 A Bayesian checklist. 3.22 Further reading. 3.23 Key points. Exercises. 4. Comparison of Alternative Approaches to Inference. 4.1 A structure for alternative approaches. 4.2 Conventional statistical methods used in health-care evaluation. 4.3 The likelihood principle, sequential analysis and types of error. 4.3.1 The likelihood principle. 4.3.2 Sequential analysis. 4.3.3 Type I and Type II error. 4.4 P-values and Bayes factors*. 4.4.1 Criticism of P-values. 4.4.2 Bayes factors as an alternative to P-values: simple hypotheses. 4.4.3 Bayes factors as an alternative to P-values: composite hypotheses. 4.4.4 Bayes factors in preference studies. 4.4.5 Lindley’s paradox. 4.5 Key points. Exercises. 5. Prior Distributions. 5.1 Introduction. 5.2 Elicitation of opinion: a brief review. 5.2.1 Background to elicitation. 5.2.2 Elicitation techniques. 5.2.3 Elicitation from multiple experts. 5.3 Critique of prior elicitation. 5.4 Summary of external evidence*. 5.5 Default priors. 5.5.1 ‘Non-informative’ or ‘reference’ priors: 5.5.2 ‘Sceptical’ priors. 5.5.3 ‘Enthusiastic’ priors. 5.5.4 Priors with a point mass at the null hypothesis (‘lump-and-smear’ priors)*. 5.6 Sensitivity analysis and ‘robust’ priors. 5.7 Hierarchical priors. 5.7.1 The judgement of exchangeability. 5.7.2 The form for the random-effects distribution. 5.7.3 The prior for the standard deviation of the random effects*. 5.8 Empirical criticism of priors. 5.9 Key points. Exercises. 6. Randomised Controlled Trials. 6.1 Introduction. 6.2 Use of a loss function: is a clinical trial for inference or decision? 6.3 Specification of null hypotheses. 6.4 Ethics and randomisation: a brief review. 6.4.1 Is randomisation necessary? 6.4.2 When is it ethical to randomise? 6.5 Sample size of non-sequential trials. 6.5.1 Alternative approaches to sample-size assessment. 6.5.2 ‘Classical power’: hybrid classical-Bayesian methods assuming normality. 6.5.3 ‘Bayesian power’. 6.5.4 Adjusting formulae for different hypotheses. 6.5.5 Predictive distribution of power and necessary sample size. 6.6 Monitoring of sequential trials. 6.6.1 Introduction. 6.6.2 Monitoring using the posterior distribution. 6.6.3 Monitoring using predictions: ‘interim power’. 6.6.4 Monitoring using a formal loss function. 6.6.5 Frequentist properties of sequential Bayesian methods. 6.6.6 Bayesian methods and data monitoring committees. 6.7 The role of ‘scepticism’ in confirmatory studies. 6.8 Multiplicity in randomised trials. 6.8.1 Subset analysis. 6.8.2 Multi-centre analysis. 6.8.3 Cluster randomization. 6.8.4 Multiple endpoints and treatments. 6.9 Using historical controls*. 6.10 Data-dependent allocation. 6.11 Trial designs other than two parallel groups. 6.12 Other aspects of drug development. 6.13 Further reading. 6.14 Key points. Exercises. 7. Observational Studies. 7.1 Introduction. 7.2 Alternative study designs. 7.3 Explicit modelling of biases. 7.4 Institutional comparisons. 7.5 Key points. Exercises. 8. Evidence Synthesis. 8.1 Introduction. 8.2 ‘Standard’ meta-analysis. 8.2.1 A Bayesian perspective. 8.2.2 Some delicate issues in Bayesian meta-analysis. 8.2.3 The relationship between treatment effect and underlying risk. 8.3 Indirect comparison studies. 8.4 Generalised evidence synthesis. 8.5 Further reading. 8.6 Key points. Exercises. 9. Cost-effectiveness, Policy-Making and Regulation. 9.1 Introduction. 9.2 Contexts. 9.3 ‘Standard’ cost-effectiveness analysis without uncertainty. 9.4 ‘Two-stage’ and integrated approaches to uncertainty in cost-effectiveness modeling. 9.5 Probabilistic analysis of sensitivity to uncertainty about parameters: two-stage approach. 9.6 Cost-effectiveness analyses of a single study: integrated approach. 9.7 Levels of uncertainty in cost-effectiveness models. 9.8 Complex cost-effectiveness models. 9.8.1 Discrete-time, discrete-state Markov models. 9.8.2 Micro-simulation in cost-effectiveness models. 9.8.3 Micro-simulation and probabilistic sensitivity analysis. 9.8.4 Comprehensive decision modeling. 9.9 Simultaneous evidence synthesis and complex cost-effectiveness modeling. 9.9.1 Generalised meta-analysis of evidence. 9.9.2 Comparison of integrated Bayesian and two-stage approach. 9.10 Cost-effectiveness of carrying out research: payback models. 9.10.1 Research planning in the public sector. 9.10.2 Research planning in the pharmaceutical industry. 9.10.3 Value of information. 9.11 Decision theory in cost-effectiveness analysis, regulation and policy. 9.12 Regulation and health policy. 9.12.1 The regulatory context. 9.12.2 Regulation of pharmaceuticals. 9.12.3 Regulation of medical devices. 9.13 Conclusions. 9.14 Key points. Exercises. 10. Conclusions and Implications for Future Research. 10.1 Introduction. 10.2 General advantages and problems of a Bayesian approach. 10.3 Future research and development. Appendix: Websites and Software. A.1 The site for this book. A.2 Bayesian methods in health-care evaluation. A.3 Bayesian software. A.4 General Bayesian sites. References. Index.

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Book SynopsisPresents methods for the design and analysis of surveys, studies, and experiments when the data is qualitative and categorical. This work also covers the delta methods for multinomial frequencies. It discusses topics in misclassification and in reliability assessment.Trade Review"A well written specialized book by Fleiss et al. illustrates in detail the definitions and importance of rates in health and other data analysis." (Journal of Statistical Computation and Simulation, April 2005) "…the definitive text of context, method and application for the efficient analysis of rates and proportions…" (Statistics in Medicine, Vol 24 (17), 15th September 2005) "…well written in a thoroughly readable style. I highly recommend this book…" (Statistical Methods in Medical Research, Vol. 14, 2005) "…persons who regularly encounter this type of data would certainly want this book available as one of their desk-top references." (Technometrics, May 2004)Table of ContentsPreface. Preface to the Second Edition. Preface to the First Edition. 1. An Introduction to Applied Probability. 2. Statistical Inference for a Single Proportion. 3. Assessing Significance in a Fourfold Table. 4. Determining Sample Sizes Needed to Detect a Difference Between Two Proportions. 5. How to Randomize. 6. Comparative Studies: Cross-Sectional, Naturalistic, or Multinomial Sampling. 7. Comparative Studies: Prospective and Retrospective Sampling. 8. Randomized Controlled Trials. 9. The Comparison of Proportions from Several Independent Samples. 10. Combining Evidence from Fourfold Tables. 11. Logistic Regression. 12. Poisson Regression. 13. Analysis of Data from Matched Samples. 14. Regression Models for Matched Samples. 15. Analysis of Correlated Binary Data. 16. Missing Data. 17. Misclassification Errors: Effects, Control, and Adjustment. 18. The Measurement of Interrater Agreement. 19. The Standardization of Rates. Appendix A. Numerical Tables. Appendix B. The Basic Theory of Maximum Likelihood Estimation. Appendix C. Answers to Selected Problems. Author Index. Subject Index.

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Book SynopsisThe subject of time series is of considerable interest, especiallyamong researchers in econometrics, engineering, and the naturalsciences. As part of the prestigious Wiley Series in Probabilityand Statistics, this book provides a lucid introduction to thefield and, in this new Second Edition, covers the importantadvances of recent years, including nonstationary models, nonlinearestimation, multivariate models, state space representations, andempirical model identification. New sections have also been addedon the Wold decomposition, partial autocorrelation, long memoryprocesses, and the Kalman filter. Major topics include: * Moving average and autoregressive processes * Introduction to Fourier analysis * Spectral theory and filtering * Large sample theory * Estimation of the mean and autocorrelations * Estimation of the spectrum * Parameter estimation * Regression, trend, and seasonality * Unit root and explosive time series To accomTable of ContentsMoving Average and Autoregressive Processes. Introduction to Fourier Analysis. Spectral Theory and Filtering. Some Large Sample Theory. Estimation of the Mean and Autocorrelations. The Periodogram, Estimated Spectrum. Parameter Estimation. Regression, Trend, and Seasonality. Unit Root and Explosive Time Series. Bibliography. Index.

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Book SynopsisDesigned to aid readers in gathering the most reliable quantitative information on forests for the least cost.Table of ContentsFocus, Fundamental Concepts, and Theory. Probabilistic Sampling Strategies. Forest Sampling--Single Level. Multi-Information Sources for Sampling. Model-Based Inference. Mensurational Aspects of Forest Inventory. Related Sampling Topics. Related Estimation Topics. Future Directions in Multiresource Sampling in Forestry. References. Answers to the Problems. Index.

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Book SynopsisQueueing theory is an effective tool for studying several performance parameters of computer systems. This book discusses the difficult subject of queuing theory is by working on information processing problems.Table of ContentsA Queueing Theory Primer. Random Processes. Birth-Death Queueing Systems. Markovian Queues. The Queue M/G/1. The Queue G/M/m. The Queue G/G/1. Index.

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Book SynopsisThis book discusses adaptive sampling designs which are used in surveys where data collection requires modification as a result of observations made during the process. The strategies detailed in the book offer solutions to the long-standing problem of estimating the abundance of rare, clustered populations.Table of ContentsFixed-Population Sampling Theory. Stochastic Population Sampling Theory. Adaptive Cluster Sampling. Efficiency and Sample Size Issues. Adaptive Cluster Sampling Based on Order Statistics. Adaptive Allocation in Stratified Sampling. Multivariate Aspects of Adaptive Sampling. Detectability in Adaptive Sampling. Optimal Sampling Strategies. References. Index.

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Book SynopsisOf related interest. Nonlinear Regression Analysis and its Applications Douglas M. Bates and Donald G. Watts . an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models. highly recommend[ed].Table of ContentsLinear Regression Analysis. Constructing and Checking the Model. Least Squares Regression. Least Absolute Deviations Regression. M-Regression. Nonparametric Regression. Bayesian Regression. Ridge Regression. Comparisons. Other Methods.

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Book SynopsisOriginally published in 1958, this text offers a simple analysis of the principles of experimental design. Emphasis is placed on basic concepts rather than the calculation of technical details. It is possible to use the book in conjunction with a text on statistical analysis.Table of ContentsPreliminaries. Some Key Assumptions. Designs for the Reduction of Error. Use of Supplementary Observations to Reduce Error. Randomization. Basic Ideas About Factorial Experiments. Design of Simple Factorial Experiments. Choice of Number of Observations. Choice of Units, Treatments, and Observations. More About Latin Squares. Incomplete Nonfactorial Designs. Fractional Replication and Confounding. Cross-Over Designs. Some Special Problems. General Bibliography. Appendix. Indexes.

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Book SynopsisSequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved.Table of ContentsPreliminaries. Sums of Independent Random Variables. Optimal Stopping. Reduction to a Single Dimension. Accessibility and Filtration Structure. Sequential Sampling. Optimal Sequential Control. Multiarmed Bandits. The Markovian Case. Optimal Switching Between Two Random Walks. Bibliography. Indexes.

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Book SynopsisThe definitive reference for statistical distributions Continuous Univariate Distributions, Volume 1 offers comprehensive guidance toward the most commonly used statistical distributions, including normal, lognormal, inverse Gaussian, Pareto, Cauchy, gamma distributions and more. Each distribution includes clear definitions and properties, plus methods of inference, applications, algorithms, characterizations, and reference to other related distributions. Organized for easy navigation and quick reference, this book is an invaluable resource for investors, data analysts, or anyone working with statistical distributions on a regular basis.Table of ContentsContinuous Distributions (General). Normal Distributions. Lognormal Distributions. Inverse Gaussian (Wald) Distributions. Cauchy Distribution. Gamma Distributions. Chi-Square Distributions Including Chi and Rayleigh. Exponential Distributions. Pareto Distributions. Weibull Distributions. Abbreviations. Indexes.

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Book SynopsisConsists of invited papers, from internationally recognized researchers, chosen for their quality as well as their overall unity. Describes current methods along with innovative research and presents new technologies for solving problems unique to establishment surveys.Table of ContentsPartial table of contents: FRAMES AND BUSINESS REGISTERS. Defining and Classifying Statistical Units (S. Nijhowne). Changes in Populations of Statistical Units (P. Struijs & A.Willeboordse). SAMPLE DESIGN AND SELECTION. Coordination of Samples Using Permanent Random Numbers (E.Ohlsson). Business Surveys as a Network Sample (A. Johnson). DATA COLLECTION AND RESPONSE QUALITY. Designing the Data Collection Process (C. Dippo, et al.). Electronic Data Interchange (C. Ambler, et al.). DATA PROCESSING. Matching and Record Linkage (W. Winkler). Protecting Confidentiality in Business Surveys (L. Cox). WEIGHTING AND ESTIMATION. Outliers in Business Surveys (H. Lee). Combining Design-Based and Model-Based Inference (K. Brewer). PAST, PRESENT, AND FUTURE DIRECTIONS. Quality Assurance for Business Surveys (G. Griffiths & S.Linacre). Business Surveys in Ten Years' Time (J. Ryten). Index.

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Book SynopsisReflecting emerging principles and trends, Measurement Errors in Surveys documents the current state of measurement errors in surveys; reports new research findings; and promotes interdisciplinary exchanges in numerous approaches in assessing, modeling and reducing measurement inaccuracies in surveys.Table of ContentsPreface. Introduction (W. Kruskal). 1. Measurement Error Across Disciplines (R. Groves). SECTION A: THE QUESTIONAIRE. 2. The Current Status of Questionnaire Design (N. Bradburn & S. Sudman). 3. Response Alternatives: The Impact of Their Choice and Presentation Order (N. Schwarz & H. Hippler). 4. Context Effects in the General Social Survey (T. Smith). 5. Mode Effects of Cognitively Designed Recall Questions: A Comparison of Answers to Telephone and Mail Surveys (D. Dillman & J. Tarnai). 6. Nonexperimental Research on Question Wording Effects: A Contribution to Solving the Generalizability Problem (N. Molenaar). 7. Measurement Errors in Business Surveys (S. Dutka & L. Frankel). SECTION B: RESPONDENTS AND RESPONSES. 8. Recall Error: Sources and Bias Reduction Techniques (D. Eisenhower, et al.). 9. Measurement Effects in Self vs. Proxy Response to Survey Questions: An Information-Processing Perspective (J. Blair, et al.). 10. An Alternative Approach to Obtaining Personal History Data (B. Means, et al.). 11. The Item Count Technique as a Method of Indirect Questioning: A Review of Its Development and a Case Study Application (J. Droitcour, et al.). 12. Toward a Response Model in Establishment Surveys (W. Edwards & D. Cantor). SECTION C: INTERVIEWERS AND OTHER MEANS OF DATA COLLECTION. 13. Data Collection Methods and Measurement Error: An Overview (L. Lyberg & D. Kasprzyk). 14. Reducing Inte5rviewer-Related Error Through Interviewer Training, Supervision, and Other Means (F. Fowler). 15. The Design and Analysis of Reinterview: An Overview (G. Forsman & I. Schreiner). 16. Expenditure Diary Surveys and Their Associated Errors (A. Silberstein & S. Scott). 17. A Review of Errors of Direct Observation in Crop Yield Surveys (R. Fecso). 18. Measurement Error in Continuing Surveys of the Grocery Retail Trade Using Electronic Data Collection Methods (J. Donmyer, et al.). SECTION D: MEASUREMENT ERRORS IN THE INTERVIEW PROCESS. 19. Conversation with a Purpose—or Conversation? Interaction in the Standardized Interview (N. Schaeffer). 20. Cognitive Laboratory Methods: A Taxonomy (B. Forsyth & J. Lessler). 21. Studying Respondent-Interviewer Interaction: The Relationship Between Interviewing Style, Interviewer Behavior, and Response Behavior (J. van der Zouwen, et al.). 22. The Effect of Interviewer and Respondent Characteristics on the Quality of Survey Data: A Multilevel Model (J. Hox, et al.). 23. Interviewer, Respondent, and Regional Office Effects on Response Variance: A Statistical Decomposition (D. Hill). SECTION E: MODELING MEASUREMENT ERRORS AND THEIR EFFECTS ON ESTIMATION AND DATA ANALYSIS. 24. Approaches to the Modeling of Measurement Errors (P. Biemer & L. Stokes). 25. A Mixed Model for Analyzing Measurement Errors for Dichotomous Variables (J. Pannekoek). 26. Models for Memory Effects in Count Data (P. van Dosselaar). 27. Simple Response Variance: Estimation and Determinants (C. O'Muircheartaigh). 28. Evaluation of Measurement Instruments Using a Structural Modeling Approach (W. Saris & F. Andrews). 29. A Path Analysis of Cross-National Data Taking Measurement Errors Into Account (I. Munck). 30. Regression Estimation in the Presence of Measurement Error (W. Fuller). 31. Chi-Squared Tests with Complex Survey Data Subject to Misclassification Error (J. Rao & D. Thomas). 32. The Effect of Measurement Error on Event History Analysis (D. Holt, et al.). References. Index.

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Book SynopsisClarifies modern data analysis through nonparametric density estimation for a complete working knowledge of the theory and methods Featuring a thoroughly revised presentation, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition maintains an intuitive approach to the underlying methodology and supporting theory of density estimation. Including new material and updated research in each chapter, the Second Edition presents additional clarification of theoretical opportunities, new algorithms, and up-to-date coverage of the unique challenges presented in the field of data analysis. The new edition focuses on the various density estimation techniques and methods that can be used in the field of big data. Defining optimal nonparametric estimators, the Second Edition demonstrates the density estimation tools to use when dealing with various multivariate structures in univariate, bivariate, trivariate, and quadrivariate data analyTrade Review"The book is an ideal reference for theoretical and applied statisticians, practicing engineers, as well as readers interested in the theoretical aspects of nonparametric estimation and the application of these methods to multivariate data. The second edition is also useful as a textbook for introductory courses in kernel statistics, smoothing, advanced computational statistics, and general forms of statistical distributions." (Zentralblatt MATH, 1 June 2015)Table of ContentsPREFACE TO SECOND EDITION xv PREFACE TO FIRST EDITION xvii 1 Representation and Geometry of Multivariate Data 1 1.1 Introduction 1 1.2 Historical Perspective 4 1.3 Graphical Display of Multivariate Data Points 5 1.3.1 Multivariate Scatter Diagrams 5 1.3.2 Chernoff Faces 11 1.3.3 Andrews’ Curves and Parallel Coordinate Curves 12 1.3.4 Limitations 14 1.4 Graphical Display of Multivariate Functionals 16 1.4.1 Scatterplot Smoothing by Density Function 16 1.4.2 Scatterplot Smoothing by Regression Function 18 1.4.3 Visualization of Multivariate Functions 19 1.4.3.1 Visualizing Multivariate Regression Functions 24 1.4.4 Overview of Contouring and Surface Display 26 1.5 Geometry of Higher Dimensions 28 1.5.1 Polar Coordinates in d Dimensions 28 1.5.2 Content of Hypersphere 29 1.5.3 Some Interesting Consequences 30 1.5.3.1 Sphere Inscribed in Hypercube 30 1.5.3.2 Hypervolume of a Thin Shell 30 1.5.3.3 Tail Probabilities of Multivariate Normal 31 1.5.3.4 Diagonals in Hyperspace 31 1.5.3.5 Data Aggregate Around Shell 32 1.5.3.6 Nearest Neighbor Distances 32 Problems 33 2 Nonparametric Estimation Criteria 36 2.1 Estimation of the Cumulative Distribution Function 37 2.2 Direct Nonparametric Estimation of the Density 39 2.3 Error Criteria for Density Estimates 40 2.3.1 MISE for Parametric Estimators 42 2.3.1.1 Uniform Density Example 42 2.3.1.2 General Parametric MISE Method with Gaussian Application 43 2.3.2 The L1 Criterion 44 2.3.2.1 L1 versus L2 44 2.3.2.2 Three Useful Properties of the L1 Criterion 44 2.3.3 Data-Based Parametric Estimation Criteria 46 2.4 Nonparametric Families of Distributions 48 2.4.1 Pearson Family of Distributions 48 2.4.2 When Is an Estimator Nonparametric? 49 Problems 50 3 Histograms: Theory and Practice 51 3.1 Sturges’ Rule for Histogram Bin-Width Selection 51 3.2 The L2 Theory of Univariate Histograms 53 3.2.1 Pointwise Mean Squared Error and Consistency 53 3.2.2 Global L2 Histogram Error 56 3.2.3 Normal Density Reference Rule 59 3.2.3.1 Comparison of Bandwidth Rules 59 3.2.3.2 Adjustments for Skewness and Kurtosis 60 3.2.4 Equivalent Sample Sizes 62 3.2.5 Sensitivity of MISE to Bin Width 63 3.2.5.1 Asymptotic Case 63 3.2.5.2 Large-Sample and Small-Sample Simulations 64 3.2.6 Exact MISE versus Asymptotic MISE 65 3.2.6.1 Normal Density 66 3.2.6.2 Lognormal Density 68 3.2.7 Influence of Bin Edge Location on MISE 69 3.2.7.1 General Case 69 3.2.7.2 Boundary Discontinuities in the Density 69 3.2.8 Optimally Adaptive Histogram Meshes 70 3.2.8.1 Bounds on MISE Improvement for Adaptive Histograms 71 3.2.8.2 Some Optimal Meshes 72 3.2.8.3 Null Space of Adaptive Densities 72 3.2.8.4 Percentile Meshes or Adaptive Histograms with Equal Bin Counts 73 3.2.8.5 Using Adaptive Meshes versus Transformation 74 3.2.8.6 Remarks 75 3.3 Practical Data-Based Bin Width Rules 76 3.3.1 Oversmoothed Bin Widths 76 3.3.1.1 Lower Bounds on the Number of Bins 76 3.3.1.2 Upper Bounds on Bin Widths 78 3.3.2 Biased and Unbiased CV 79 3.3.2.1 Biased CV 79 3.3.2.2 Unbiased CV 80 3.3.2.3 End Problems with BCV and UCV 81 3.3.2.4 Applications 81 3.4 L2 Theory for Multivariate Histograms 83 3.4.1 Curse of Dimensionality 85 3.4.2 A Special Case: d = 2 with Nonzero Correlation 87 3.4.3 Optimal Regular Bivariate Meshes 88 3.5 Modes and Bumps in a Histogram 89 3.5.1 Properties of Histogram “Modes” 91 3.5.2 Noise in Optimal Histograms 92 3.5.3 Optimal Histogram Bandwidths for Modes 93 3.5.4 A Useful Bimodal Mixture Density 95 3.6 Other Error Criteria: L1,L4,L6,L8, and L∞ 96 3.6.1 Optimal L1 Histograms 96 3.6.2 Other LP Criteria 97 Problems 97 4 Frequency Polygons 100 4.1 Univariate Frequency Polygons 101 4.1.1 Mean Integrated Squared Error 101 4.1.2 Practical FP Bin Width Rules 104 4.1.3 Optimally Adaptive Meshes 107 4.1.4 Modes and Bumps in a Frequency Polygon 109 4.2 Multivariate Frequency Polygons 110 4.3 Bin Edge Problems 113 4.4 Other Modifications of Histograms 114 4.4.1 Bin Count Adjustments 114 4.4.1.1 Linear Binning 114 4.4.1.2 Adjusting FP Bin Counts to Match Histogram Areas 117 4.4.2 Polynomial Histograms 117 4.4.3 How Much Information Is There in a Few Bins? 120 Problems 122 5 Averaged Shifted Histograms 125 5.1 Construction 126 5.2 Asymptotic Properties 128 5.3 The Limiting ASH as a Kernel Estimator 133 Problems 135 6 Kernel Density Estimators 137 6.1 Motivation for Kernel Estimators 138 6.1.1 Numerical Analysis and Finite Differences 138 6.1.2 Smoothing by Convolution 139 6.1.3 Orthogonal Series Approximations 140 6.2 Theoretical Properties: Univariate Case 142 6.2.1 MISE Analysis 142 6.2.2 Estimation of Derivatives 144 6.2.3 Choice of Kernel 145 6.2.3.1 Higher Order Kernels 145 6.2.3.2 Optimal Kernels 151 6.2.3.3 Equivalent Kernels 153 6.2.3.4 Higher Order Kernels and Kernel Design 155 6.2.3.5 Boundary Kernels 157 6.3 Theoretical Properties: Multivariate Case 161 6.3.1 Product Kernels 162 6.3.2 General Multivariate Kernel MISE 164 6.3.3 Boundary Kernels for Irregular Regions 167 6.4 Generality of the Kernel Method 167 6.4.1 Delta Methods 167 6.4.2 General Kernel Theorem 168 6.4.2.1 Proof of General Kernel Result 168 6.4.2.2 Characterization of a Nonparametric Estimator 169 6.4.2.3 Equivalent Kernels of Parametric Estimators 171 6.5 Cross-Validation 172 6.5.1 Univariate Data 172 6.5.1.1 Early Efforts in Bandwidth Selection 173 6.5.1.2 Oversmoothing 176 6.5.1.3 Unbiased and Biased Cross-Validation 177 6.5.1.4 Bootstrapping Cross-Validation 181 6.5.1.5 Faster Rates and PI Cross-Validation 184 6.5.1.6 Constrained Oversmoothing 187 6.5.2 Multivariate Data 190 6.5.2.1 Multivariate Cross-Validation 190 6.5.2.2 Multivariate Oversmoothing Bandwidths 191 6.5.2.3 Asymptotics of Multivariate Cross-Validation 192 6.6 Adaptive Smoothing 193 6.6.1 Variable Kernel Introduction 193 6.6.2 Univariate Adaptive Smoothing 195 6.6.2.1 Bounds on Improvement 195 6.6.2.2 Nearest-Neighbor Estimators 197 6.6.2.3 Sample-Point Adaptive Estimators 198 6.6.2.4 Data Sharpening 200 6.6.3 Multivariate Adaptive Procedures 202 6.6.3.1 Pointwise Adapting 202 6.6.3.2 Global Adapting 203 6.6.4 Practical Adaptive Algorithms 204 6.6.4.1 Zero-Bias Bandwidths for Tail Estimation 204 6.6.4.2 UCV for Adaptive Estimators 208 6.7 Aspects of Computation 209 6.7.1 Finite Kernel Support and Rounding of Data 210 6.7.2 Convolution and Fourier Transforms 210 6.7.2.1 Application to Kernel Density Estimators 211 6.7.2.2 FFTs 212 6.7.2.3 Discussion 212 6.8 Summary 213 Problems 213 7 The Curse of Dimensionality and Dimension Reduction 217 7.1 Introduction 217 7.2 Curse of Dimensionality 220 7.2.1 Equivalent Sample Sizes 220 7.2.2 Multivariate L1 Kernel Error 222 7.2.3 Examples and Discussion 224 7.3 Dimension Reduction 229 7.3.1 Principal Components 229 7.3.2 Projection Pursuit 231 7.3.3 Informative Components Analysis 234 7.3.4 Model-Based Nonlinear Projection 239 Problems 240 8 Nonparametric Regression and Additive Models 241 8.1 Nonparametric Kernel Regression 242 8.1.1 The Nadaraya–Watson Estimator 242 8.1.2 Local Least-Squares Polynomial Estimators 243 8.1.2.1 Local Constant Fitting 243 8.1.2.2 Local Polynomial Fitting 244 8.1.3 Pointwise Mean Squared Error 244 8.1.4 Bandwidth Selection 247 8.1.5 Adaptive Smoothing 247 8.2 General Linear Nonparametric Estimation 248 8.2.1 Local Polynomial Regression 248 8.2.2 Spline Smoothing 250 8.2.3 Equivalent Kernels 252 8.3 Robustness 253 8.3.1 Resistant Estimators 254 8.3.2 Modal Regression 254 8.3.3 L1 Regression 257 8.4 Regression in Several Dimensions 259 8.4.1 Kernel Smoothing and WARPing 259 8.4.2 Additive Modeling 261 8.4.3 The Curse of Dimensionality 262 8.5 Summary 265 Problems 266 9 Other Applications 267 9.1 Classification, Discrimination, and Likelihood Ratios 267 9.2 Modes and Bump Hunting 273 9.2.1 Confidence Intervals 273 9.2.2 Oversmoothing for Derivatives 275 9.2.3 Critical Bandwidth Testing 275 9.2.4 Clustering via Mixture Models and Modes 277 9.2.4.1 Gaussian Mixture Modeling 277 9.2.4.2 Modes for Clustering 280 9.3 Specialized Topics 286 9.3.1 Bootstrapping 286 9.3.2 Confidence Intervals 287 9.3.3 Survival Analysis 289 9.3.4 High-Dimensional Holes 290 9.3.5 Image Enhancement 292 9.3.6 Nonparametric Inference 292 9.3.7 Final Vignettes 293 9.3.7.1 Principal Curves and Density Ridges 293 9.3.7.2 Time Series Data 294 9.3.7.3 Inverse Problems and Deconvolution 294 9.3.7.4 Densities on the Sphere 294 Problems 294 APPENDIX A Computer Graphics in R3 296 A.1 Bivariate and Trivariate Contouring Display 296 A.1.1 Bivariate Contouring 296 A.1.2 Trivariate Contouring 299 A.2 Drawing 3-D Objects on the Computer 300 APPENDIX B DataSets 302 B.1 US Economic Variables Dataset 302 B.2 University Dataset 304 B.3 Blood Fat Concentration Dataset 305 B.4 Penny Thickness Dataset 306 B.5 Gas Meter Accuracy Dataset 307 B.6 Old Faithful Dataset 309 B.7 Silica Dataset 309 B.8 LRL Dataset 310 B.9 Buffalo Snowfall Dataset 310 APPENDIX C Notation and Abbreviations 311 C.1 General Mathematical and Probability Notation 311 C.2 Density Abbreviations 312 C.3 Error Measure Abbreviations 313 C.4 Smoothing Parameter Abbreviations 313 REFERENCES 315 AUTHOR INDEX 334 SUBJECT INDEX 339

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